P. Kloeden

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Numerical Solution of Stochastic Differential Equations

P. Kloeden, E. Platen, 1992 .

Numerical Solutions of Stochastic Differential Equations

P. Kloeden, E. Platen, 1995 .

Strong convergence of an explicit numerical method for SDEs with nonglobally Lipschitz continuous coefficients

P. Kloeden, M. Hutzenthaler, Arnulf Jentzen, 2010, 1010.3756.

Strong and weak divergence in finite time of Euler's method for stochastic differential equations with non-globally Lipschitz continuous coefficients

P. Kloeden, M. Hutzenthaler, Arnulf Jentzen, 2009, Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences.

Metric spaces of fuzzy sets

P. Kloeden, P. Diamond, 1990 .

Metric Spaces Of Fuzzy Sets Theory And Applications

P. Kloeden, P. Diamond, Dingwei Zheng, 1975 .

Collapsing effects in numerical simulation of a class of chaotic dynamical systems and random mappings with a single attracting centre

P. Kloeden, A. Vladimirov, P. Diamond, 1995 .

An invariant measure arising in computer simulation of a chaotic dynamical system

P. Kloeden, P. Diamond, A. Pokrovskii, 1994 .

Remarks on Peano-like theorems for fuzzy differential equations

P. Kloeden, 1991 .

From Elementary Probability to Stochastic Differential Equations with MAPLE

P. Kloeden, S. Cyganowski, J. Ombach, 2001 .

The Pathwise Convergence of Approximation Schemes for Stochastic Differential Equations

P. Kloeden, A. Neuenkirch, 2007, LMS J. Comput. Math..

Forward attraction in nonautonomous difference equations

P. Kloeden, Meihua Yang, 2016 .

Fuzzy dynamical systems

P. Kloeden, 1982 .

Metric Topology of Fuzzy Numbers and Fuzzy Analysis

P. Kloeden, P. Diamond, 2000 .

Upper semicontinuous dependence of pullback attractors on time scales

P. Kloeden, 2006 .

A Gronwall-like Inequality and Continuous Dependence on Time Scales

P. Kloeden, 2003 .

A Random Model for Immune Response to Virus in Fluctuating Environments

P. Kloeden, T. Caraballo, Y. Asai, 2016 .

Wu, Fuke and Mao, Xuerong and Kloeden, Peter E. (2013) Discrete Razumikhin-type technique and stability of the Euler-Maruyama method to stochastic functional differential equations. Discrete and Continuous Dynamical Systems

P. Kloeden, X. Mao, Fuke Wu, 2018 .

Discrete Razumikhin-type technique and stability of the Euler-Maruyama method to stochastic functional differential equations

P. Kloeden, X. Mao, Fuke Wu, 2012 .

Semi-Hyperbolicity and Bi-Shadowing

P. Kloeden, P. Imkeller, P. Diamond, 2010 .

Overcoming the order barrier in the numerical approximation of stochastic partial differential equations with additive space–time noise

P. Kloeden, Arnulf Jentzen, 2009, Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences.

TAYLOR EXPANSIONS OF SOLUTIONS OF STOCHASTIC PARTIAL DIFFERENTIAL EQUATIONS WITH ADDITIVE NOISE

P. Kloeden, Arnulf Jentzen, 2009, 1010.0161.

Strong convergence rates for explicit space-time discrete numerical approximations of stochastic Allen-Cahn equations

P. Kloeden, Arnulf Jentzen, B. Gess, 2017, Stochastics and Partial Differential Equations: Analysis and Computations.

The approximation of multiple stochastic integrals

P. Kloeden, E. Platen, I. W. Wright, 1992 .

Taylor Approximations for Stochastic Partial Differential Equations

P. Kloeden, Arnulf Jentzen, 2011 .

Time-discretised Galerkin approximations of parabolic stochastic PDE's

P. Kloeden, W. Grecksch, 1996, Bulletin of the Australian Mathematical Society.

LINEAR-IMPLICIT STRONG SCHEMES FOR ITO-GALKERIN APPROXIMATIONS OF STOCHASTIC PDES

P. Kloeden, S. Shott, 2001 .

Pathwise convergent higher order numerical schemes for random ordinary differential equations

P. Kloeden, Arnulf Jentzen, 2007, Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences.

The Numerical Approximation of Stochastic Partial Differential Equations

P. Kloeden, Arnulf Jentzen, 2009 .

Numerical Solution of Sde Through Computer Experiments

P. Kloeden, E. Platen, H. Schurz, 1993 .

Stochastic Differential Equations with Nonlocal Sample Dependence

P. Kloeden, Thomas Lorenz, 2010 .

CONVERGENCE AND STABILITY OF IMPLICIT METHODS FOR JUMP-DIFFUSION SYSTEMS

P. Kloeden, D. Higham, 2005 .

Exponentially Stable Stationary Solutions for Stochastic Evolution Equations and Their Perturbation

P. Kloeden, T. Caraballo, B. Schmalfuß, 2004 .

Higher-order implicit strong numerical schemes for stochastic differential equations

P. Kloeden, E. Platen, 1992 .

Relations between multiple ito and stratonovich integrals

P. Kloeden, E. Platen, 1991 .

Eventual stability in general control systems

P. Kloeden, 1975 .

Stable attracting sets in dynamical systems and in their one-step discretizations

P. Kloeden, J. Lorenz, 1986 .

The inflation of attractors and their discretization: the autonomous case

P. Kloeden, V. Kozyakin, 2000 .

Extrapolation methods for the weak approximation of Ito diffusions

Peter E. Kloeden, Eckhard Platen, P. Kloeden, 1995 .

Random attractors for stochastic semi-linear degenerate parabolic equations

Peter E. Kloeden, Meihua Yang, P. Kloeden, 2011 .

Nonautonomous Dynamical Systems

Peter E. Kloeden, Martin Rasmussen, M. Rasmussen, 2011 .

Chaotic difference equations in Rn

Peter E. Kloeden, P. Kloeden, 1981 .

Artificial Life Extension

P. Kloeden, O. Rössler, R. Roessler, 1994 .

CONVERGENCE OF NUMERICAL METHODS FOR STOCHASTIC DIFFERENTIAL EQUATIONS IN MATHEMATICAL FINANCE

Andreas Neuenkirch, Peter Kloeden, P. Kloeden, 2012, 1204.6620.

Synchronization of systems of Marcus canonical equations driven by α-stable noises☆

Peter E. Kloeden, Jinqiao Duan, Jicheng Liu, 2010 .

Characterization of compact subsets of fuzzy sets

Peter E. Kloeden, Phil Diamond, P. Kloeden, 1989 .

Nonautonomous Dynamical Systems in the Life Sciences

Peter E. Kloeden, Christian Pötzsche, P. Kloeden, 2013 .

EXISTENCE AND UNIQUENESS THEOREMS FOR FBM STOCHASTIC DIFFERENTIAL EQUATIONS

P. Kloeden, V. Anh, M. Kleptsyna, 1998 .

Sigmoidal approximations of Heaviside functions in neural lattice models

P. Kloeden, Xiaoying Han, 2020 .

Asymptotic behavior of a neural field lattice model with a Heaviside operator

P. Kloeden, Xiaoying Han, 2019, Physica D: Nonlinear Phenomena.

Lattice Dynamical Systems in the Biological Sciences

P. Kloeden, Xiaoying Han, 2019, Modeling, Stochastic Control, Optimization, and Applications.

Runge-Kutta methods for affinely controlled nonlinear systems

P. Kloeden, Andreas Röíler, 2007 .

Synchronization of Dissipative Dynamical Systems Driven by Non-Gaussian Lévy Noises

P. Kloeden, Jinqiao Duan, Jicheng Liu, 2009, 0901.2446.

Dynamics of Nonautonomous Chemostat Models

P. Kloeden, Alain Rapaport, T. Caraballo, 2015 .

Statistical properties of some spatially discretized dynamical systems

P. Kloeden, J. Mustard, A. Pokrovski, 1999 .

A model for roundoff and collapse in computation of chaotic dynamical systems

P. Kloeden, P. Diamond, V. Kozyakin, 1997 .

Resource Game: Present Bias and Sophisticated Paradigm

P. Kloeden, Ling Peng, 2021, Environmental Modeling & Assessment.

A Peano-Like Theorem for Stochastic Differential Equations with Nonlocal Sample Dependence

P. Kloeden, Thomas Lorenz, 2013 .

Negatively Invariant Sets and Entire Trajectories of Set-Valued Dynamical Systems

P. Kloeden, P. Marín-Rubio, 2011 .

Attractors of Weakly Asymptotically Compact Set-Valued Dynamical Systems

P. Kloeden, J. Valero, 2005 .

Weak pullback attractors of setvalued processes

P. Kloeden, T. Caraballo, P. Marín-Rubio, 2003 .

Converse theorems for stochastic exponential stability

P. Kloeden, P. Diamond, 1977 .

Runge–Kutta Methods for Monotone Differential and Delay Equations

P. Kloeden, J. Schropp, 2003 .

On general semi dynamical systems

Peter E. Kloeden, P. Kloeden, 1975, Bulletin of the Australian Mathematical Society.

Stochastic morphological evolution equations

P. Kloeden, Thomas Lorenz, 2011 .

Li–Yorke chaos in higher dimensions: a review

Peter E. Kloeden, Zhong Li, P. Kloeden, 2006 .

Beyond the Li-Yorke Definition of Chaos

P. Kloeden, Zhong Li, 2006 .

Asymptotic behaviour of dynamical systems with plastic self-organising vector fields

P. Kloeden, N. Janson, 2018, 1812.05205.

Mean anisotropy of homogeneous Gaussian random fields and anisotropic norms of linear translation-invariant operators on multidimensional integer lattices.

P. Kloeden, P. Diamond, I. Vladimirov, 2003 .

Synchronization in coupled stochastic sine-Gordonwave model

P. Kloeden, Meihua Yang, I. Chueshov, 2016 .

Numerical dynamics of integrodifference equations: Forward dynamics and pullback attractors

P. Kloeden, H. Huynh, Christian Potzsche, 2022, Journal of Computational Dynamics.

Analysis of an algorithm for computing invariant measures

P. Kloeden, P. Diamond, A. Pokrovskii, 1995 .

Dissipative synchronization of nonautonomous and random systems

P. Kloeden, R. Pavani, 2009 .

Synchronization of Systems with Multiplicative Noise

P. Kloeden, T. Caraballo, A. Neuenkirch, 2008 .

Long term dynamics of second order-in-time stochastic evolution equations with state-dependent delay

P. Kloeden, Meihua Yang, I. Chueshov, 2018 .

Pullback attractors for stochastic recurrent neural networks with discrete and distributed delays

P. Kloeden, Yejuan Wang, Meiyu Sui, 2021, Electronic Research Archive.

Attractors of Hopfield-type lattice models with increasing neuronal input

P. Kloeden, Xiaoying Han, Xiaoli Wang, 2020, Discrete & Continuous Dynamical Systems - B.

The asymptotic behaviour of fractional lattice systems with variable delay

P. Kloeden, T. Caraballo, Linfang Liu, 2019, Fractional Calculus and Applied Analysis.

Asymptotic behavior of stochastic lattice systems with a Caputo fractional time derivative

P. Kloeden, Jiaohui Xu, Yejuan Wang, 2016 .

IMPULSIVE FRACTIONAL FUNCTIONAL DIFFERENTIAL EQUATIONS WITH A WEAKLY CONTINUOUS NONLINEARITY

P. Kloeden, Yejuan Wang, Fengshuang Gao, 2017 .

Random recurrent neural networks with delays

P. Kloeden, Xiaoying Han, Yejuan Wang, 2020 .

A reusable discounting framework under jump-diffusion process

P. Kloeden, Ling Peng, 2022, Expert Syst. Appl..

Asymptotic behaviour of the nonautonomous SIR equations with diffusion

P. Kloeden, M. Anguiano, 2013 .

Random Attractors and the Preservation of Synchronization in the Presence of Noise

P. Kloeden, 2007 .

Stabilization of Stationary Solutions of Evolution Equations by Noise

P. Kloeden, T. Caraballo, B. Schmalfuß, 2006 .

Chemostats with time-dependent inputs and wall growth

Tomás Caraballo Garrido, P. Kloeden, Han Xiaoying, 2015 .

An elliptic boundary-value problem with a discontinuous nonlinearity, II

P. Kloeden, G. Keady, 1987, Proceedings of the Royal Society of Edinburgh: Section A Mathematics.

Mathematical Consistency and Long-Term Behaviour of a Dynamical System with a Self-Organising Vector Field

P. Kloeden, N. Janson, 2020, Journal of Dynamics and Differential Equations.

Nonlocal multi-scale traffic flow models: analysis beyond vector spaces

P. Kloeden, Thomas Lorenz, 2016 .

Numerical Solution of Sde Through Computer Experiments

P. Kloeden, E. Platen, H. Schurz, 1993 .

Invariant forward attractors of non-autonomous random dynamical systems

P. Kloeden, Hongyong Cui, 2018, Journal of Differential Equations.

Asymptotic invariance and the discretisation of nonautonomous forward attracting sets

P. Kloeden, 2017 .

An Introduction to Nonautonomous Dynamical Systems and their Attractors

P. Kloeden, Meihua Yang, 2020 .

Forward omega limit sets of nonautonomous dynamical systems

P. Kloeden, Meihua Yang, Hongyong Cui, 2020, Discrete & Continuous Dynamical Systems - S.

Mean-square convergence of numerical methods for random ordinary differential equations

P. Kloeden, Peng Wang, Yanzhao Cao, 2020, Numerical Algorithms.

The numerical solution of random ODEs

P. Kloeden, Xiaoying Han, 2018 .

Asymptotic behaviour of a neural field lattice model with delays

P. Kloeden, Meihua Yang, Xiaoli Wang, 2020, Electronic Research Archive.

Sigmoidal approximations of a delay neural lattice model with Heaviside functions

P. Kloeden, Meihua Yang, Xiaoli Wang, 2020, Communications on Pure & Applied Analysis.

Equi-Attraction and Continuous Dependence of Strong Attractors of Set-Valued Dynamical Systems on Parameters

P. Kloeden, Desheng Li, 2005 .

Pathwise upper semi-continuity of random pullback attractors along the time axis

P. Kloeden, Fuke Wu, Hongyong Cui, 2018, Physica D: Nonlinear Phenomena.

Nonautonomous Attractors

P. Kloeden, Meihua Yang, 2021, Understanding Complex Systems.

Attractors of asymptotically autonomous quasi-linear parabolic equation with spatially variable exponents

P. Kloeden, J. Simsen, 2015 .

The mean-square dichotomy spectrum and a bifurcation to a mean-square attractor

T. S. Doan, M. Rasmussen, P. Kloeden, 2014, 1403.1068.

Discrete convergence and the equivalence of equi-attraction and the continuous convergence of attractors

P. Kloeden, S. Piskarev, 2007 .

Pitchfork and transcritical bifurcations in systems with homogeneous nonlinearities and an almost periodic time coefficient

P. Kloeden, 2004 .

CHAOTIC DIFFERENCE EQUATIONS IN R"

P. Kloeden, H. Lausch, 2008 .

Chaotic dynamics in nonsmooth perturbations of bishadowing systems

P. Kloeden, M. Krasnosel’skiǐ, P. Diamond, 2000 .

Asymptotic behavior of coupled inclusions with variable exponents

P. Kloeden, P. Wittbold, J. Simsen, 2020, Communications on Pure & Applied Analysis.

Attractors of set-valued partial differential equations under discretization

P. Kloeden, J. Valero, 2009 .

Upper semi continuity of attractors of delay differential equations in the delay

P. Kloeden, 2006 .

Long term behavior of a random Hopfield neural lattice model

P. Kloeden, Xiaoying Han, B. Usman, 2019, Communications on Pure & Applied Analysis.

Sequence Spaces with Variable Exponents for Lattice Systems with Nonlinear Diffusion

P. Kloeden, Xiaoying Han, J. Simsen, 2018, Understanding Complex Systems.

Attractors Under Discretisation

P. Kloeden, Xiaoying Han, 2017 .

Random Ordinary Differential Equations

P. Kloeden, Xiaoying Han, 2017 .

Uniform attractors of periodic and asymptotically periodic dynamical systems

P. Kloeden, Desheng Li, C. Zhong, 2004 .

Random Ordinary Differential Equations and Their Numerical Solution

Xiaoying Han, Peter E. Kloeden, P. Kloeden, 2017 .

The dynamics of epidemiological systems with nonautonomous and random coefficients

P. Kloeden, V. Kozyakin, 2011 .

Lower and upper bounds for strong approximation errors for numerical approximations of stochastic heat equations

P. Kloeden, Arnulf Jentzen, B. Gess, 2020, BIT Numerical Mathematics.

Semi-Dynamical Systems Generated by Autonomous Caputo Fractional Differential Equations

T. S. Doan, P. Kloeden, 2021, Vietnam Journal of Mathematics.

Mathematical Consistency and Long-Term Behaviour of a Dynamical System with a Self-Organising Vector Field

P. Kloeden, N. Janson, 2020, Journal of Dynamics and Differential Equations.

Numerical schemes for random ODEs with affine noise

P. Kloeden, Y. Asai, Yusuke Asai, 2016, Numerical Algorithms.

A survey of numerical methods for stochastic differential equations

Peter E. Kloeden, Eckhard Platen, P. Kloeden, 1989 .

The funnel boundary of multivalued dynamical systems

P. Kloeden, 1979, Journal of the Australian Mathematical Society.

Dynamics of continuous-time recurrent neural networks with random connection weights and unbounded distributed delays

Yejuan Wang, Meiyu Sui, Xiaoying Han, 2021, The European Physical Journal Plus.

Discretization of Asymptotically Stable Stationary Solutions of Delay Differential Equations with a Random Stationary Delay

P. Kloeden, T. Caraballo, J. Real, 2006 .

Nonautonomous and Random Attractors

P. Kloeden, H. Crauel, 2015, Jahresbericht der Deutschen Mathematiker-Vereinigung.

Nonautonomous and Random Attractors

P. Kloeden, H. Crauel, 2015 .

Discrete-Time Nonautonomous Dynamical Systems

Peter E. Kloeden, Martin Rasmussen, Christian Pötzsche, 2013 .

RANDOM ATTRACTORS OF STOCHASTIC REACTION–DIFFUSION EQUATIONS ON VARIABLE DOMAINS

Peter E. Kloeden, Hans Crauel, Meihua Yang, 2011 .

Discretization of Stationary Solutions of Stochastic Systems Driven by Fractional Brownian Motion

Peter E. Kloeden, Andreas Neuenkirch, María J. Garrido-Atienza, 2009 .

Lyapunov's second method for nonautonomous differential equations

Stefan Siegmund, Lars Grüne, Peter E. Kloeden, 2007 .

Flattening, squeezing and the existence of random attractors

Peter E. Kloeden, José A. Langa, P. Kloeden, 2007, Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences.

Nonautonomous bifurcation scenarios in SIR models

P. Kloeden, C. Pötzsche, 2015 .

Robustness of a dynamical systems model with a plastic self-organising vector field to noisy input signals

N. B. Janson, P. E. Kloeden, P. Kloeden, 2021, The European Physical Journal Plus.

Construction of nonautonomous forward attractors

P. Kloeden, Thomas Lorenz, 2015 .

Pullback and Forward Attractors of Nonautonomous Difference Equations

P. Kloeden, Thomas Lorenz, 2015 .

Limitations of pullback attractors for processes

Peter E. Kloeden, Martin Rasmussen, Christian Pötzsche, 2012 .

Negatively Invariant Sets and Entire Solutions

P. Kloeden, P. Marín-Rubio, 2011 .

Bifurcations and Continuous Transitions of attractors in Autonomous and nonautonomous Systems

Stefan Siegmund, Peter E. Kloeden, P. Kloeden, 2005, Int. J. Bifurc. Chaos.

UNIFORM NONAUTONOMOUS ATTRACTORS UNDER DISCRETIZATION

P. Kloeden, V. Kozyakin, 2003 .

PULLBACK ATTRACTORS OF NONAUTONOMOUS SEMIDYNAMICAL SYSTEMS

P. Kloeden, 2003 .

TWO-STEP TRANSITION IN NONAUTONOMOUS BIFURCATIONS: AN EXPLANATION

P. Kloeden, Russell Johnson, R. Pavani, 2002 .

Pullback attractors in nonautonomous difference equations

Peter E. Kloeden, P. Kloeden, 2000 .

Towards a Theory of Random Numerical Dynamics

Peter E. Kloeden, Björn Schmalfuß, P. Kloeden, 1999 .

Cocycle Attractors of Variable Time-Step Discretizations of Lorenzian Systems ∗

Peter E. Kloeden, P. Kloeden, B. Schmalfuß, 1997 .

Lyapunov functions and attractors under variable time-step discretization

Peter E. Kloeden, Björn Schmalfuss, P. Kloeden, 1996 .

A Lyapunov function for pullback attractors of nonautonomous differential equations ∗

P. Kloeden, 2022 .

Recent Developments in Dynamical Systems: Three Perspectives

Peter E. Kloeden, Francisco Balibrea, Tomás Caraballo, 2010, Int. J. Bifurc. Chaos.

Timekeeping in genetically programmed aging

P. Kloeden, O. Rössler, R. Rössler, 1993, Experimental Gerontology.

A nonautonomous chemostat model for the growth of gut microbiome with varying nutrient

P. Kloeden, Xiaoying Han, H. Wyk, 2022, Discrete & Continuous Dynamical Systems - S.

Introduction to Stochastic Time Discrete Approximation

Eckhard Platen, Peter E. Kloeden, P. Kloeden, 1992 .

Modelling with Stochastic Differential Equations

P. Kloeden, E. Platen, 1992 .

Applications of Stochastic Differential Equations

Peter E. Kloeden, Eckhard Platen, P. Kloeden, 1992 .

Convergence Rate of Random Attractors for 2D Navier–Stokes Equation Towards the Deterministic Singleton Attractor

P. Kloeden, Hongyong Cui, 2020 .

Asymptotic behaviour of random tridiagonal Markov chains in biological applications

P. Kloeden, V. Kozyakin, 2011, 1112.5844.

A Peano theorem for fuzzy differential equations with evolving membership grade

Thomas Lorenz, Peter E. Kloeden, P. Kloeden, 2015, Fuzzy Sets Syst..

Reaction-diffusion equations with a switched--off reaction zone

P. Kloeden, Meihua Yang, Thomas Lorenz, 2014 .

Dissipative quasigeostrophic motion and ocean modelling

P. Kloeden, A. Bennett, 1981 .

Human memory as ap-adic dynamic system

Sergio Albeverio, Peter E. Kloeden, A. Khrennikov, 1998 .

Interval stochastic matrices: A combinatorial lemma and the computation of invariant measures of dynamical systems

P. Kloeden, P. Diamond, A. Pokrovskii, 1995 .

Generalised Markovian control systems

Peter E. Kloeden, P. Kloeden, 1974, Journal of the Australian Mathematical Society.

Probability and Statistics

Peter E. Kloeden, Eckhard Platen, P. Kloeden, 1992 .

Transitive Limit Closures of Convex Dynamical Systems

P. Kloeden, A. Vladimirov, P. Diamond, 1998 .

Nonautonomous attractors of switching systems

P. E. Kloeden, P. Kloeden, 2006 .

SYNCHRONIZATION OF NONAUTONOMOUS DYNAMICAL SYSTEMS

Peter E. Kloeden, P. Kloeden, 2003 .

Hyperbolic homeomorphisms and bishadowing

P. Kloeden, P. Kloeden, J. Ombach, 1997 .

Lyapunov functions for linear nonautonomous dynamical equations on time scales

P. Kloeden, Alexandra Zmorzynska, 2006 .

Chaotic difference equations are dense

P. Kloeden, 1976, Bulletin of the Australian Mathematical Society.

Continuous and Inverse Shadowing

Peter E. Kloeden, P. Kloeden, J. Ombach, 2004 .

Expansivity of semi-hyperbolic Lipschitz mappings

P. Kloeden, P. Diamond, V. Kozyakin, 1995, Bulletin of the Australian Mathematical Society.

Asymptotic separation between solutions of Caputo fractional stochastic differential equations

H. T. Tuan, Doan Thai Son, P. Kloeden, 2017, 1711.08622.

Semi-Dynamical Systems Generated by Autonomous Caputo Fractional Differential Equations

Peter E. Kloeden, T. S. Doan, P. Kloeden, 2019, Vietnam Journal of Mathematics.

Mean-square random dynamical systems

Peter E. Kloeden, P. Kloeden, Thomas Lorenz, 2012, An Introduction to Nonautonomous Dynamical Systems and their Attractors.

Pathwise Taylor schemes for random ordinary differential equations

Peter E. Kloeden, Arnulf Jentzen, P. Kloeden, 2009 .

Numerical Schemes of Higher Order for a Class of Nonlinear Control Systems

Lars Grüne, Peter E. Kloeden, L. Grüne, 2002, Numerical Methods and Application.

Asymptotic behavior of solutions for random wave equations with nonlinear damping and white noise

Peter E. Kloeden, Jinqiao Duan, Meihua Yang, 2011 .

Synchronization of a Stochastic Reaction-Diffusion System on a Thin Two-Layer Domain

Peter E. Kloeden, Tomás Caraballo, Igor D. Chueshov, 2007, SIAM J. Math. Anal..

The minimal center of attraction of measurable systems and their discretizations

P. Kloeden, P. Diamond, A. Pokrovskii, 1996 .

On the dynamics of nonautonomous periodic general dynamical systems and differential inclusions

Desheng Li, Peter E. Kloeden, P. Kloeden, 2006 .

On the asymptotical behavior of nonautonomous dynamical systems

Peter E. Kloeden, Li Desheng, P. Kloeden, 2004 .

Asymptotic invariance and limit sets of general control systems

Peter E. Kloeden, P. Kloeden, 1975 .

Robustness of asymptotic stability to small time delays

P. Kloeden, Desheng Li, 2005 .

Global exponential κ -dissipative semigroups and exponential attraction

P. Kloeden, Meihua Yang, C. Zhong, 2017 .

Random attractors of a stochastic Hopfield neural network model with delays

P. Kloeden, Quanxin Zhu, Wenjie Hu, 2023, 2302.05504.

Stochastic dynamics of a neural field lattice model with state dependent nonlinear noise

Xiaoying Han, Peter E. Kloeden, Xiaoli Wang, 2021, Nonlinear Differential Equations and Applications NoDEA.

Pullback Exponential Attractors for Non-autonomous Recurrent Neural Networks with Discrete and Distributed Time-Varying Delays

Yejuan Wang, Peter E. Kloeden, Lin Yang, 2021, Journal of Dynamics and Differential Equations.

Mean-square random attractors of stochastic delay differential equations with random delay

Peter E. Kloeden, Fuke Wu, P. Kloeden, 2013 .

Numerical methods for nonlinear stochastic differential equations with jumps

Desmond J. Higham, Peter E. Kloeden, P. Kloeden, 2005, Numerische Mathematik.

Efficient simulation of nonlinear parabolic SPDEs with additive noise

Arnulf Jentzen, Peter Kloeden, P. Kloeden, 2011, 1210.8320.

Strong convergence rates for backward Euler on a class of nonlinear jump-diffusion problems

Desmond J. Higham, Peter E. Kloeden, P. Kloeden, 2007 .

Electronic Journal of Qualitative Theory of Differential Equations

P. Kloeden, J. Simsen, 2021 .

Pathwise approximation of stochastic differential equations on domains: higher order convergence rates without global Lipschitz coefficients

Peter E. Kloeden, Arnulf Jentzen, Andreas Neuenkirch, 2009, Numerische Mathematik.

Higher order numerical schemes for affinely controlled nonlinear systems

Lars Grüne, Peter E. Kloeden, L. Grüne, 2001, Numerische Mathematik.

Nonautonomous Chemostats with Variable Delays

Xiaoying Han, Peter E. Kloeden, Tomás Caraballo, 2015, SIAM J. Math. Anal..

Numerical schemes for ordinary delay differential equations with random noise

Yusuke Asai, Peter E. Kloeden, P. Kloeden, 2019, Appl. Math. Comput..

Recent Developments in Computational Finance: Foundations, Algorithms and Applications

Thomas Gerstner, Peter E. Kloeden, P. Kloeden, 2013 .

Cycles of Spatial Discretizations of Shadowing Dynamical Systems

P. Kloeden, P. Diamond, A. Pokrovskii, 1995 .

Weak Pullback Attractors of Non-autonomous Difference Inclusions

Peter E. Kloeden, Pedro Marín-Rubio, P. Kloeden, 2003 .

Does a centralized clock for ageing exist?

O E Rössler, P E Kloeden, P. Kloeden, 1990, Gerontology.

Gauss-Quadrature Method for One-Dimensional Mean-Field SDEs

Tony Shardlow, Peter Kloeden, P. Kloeden, 2016, SIAM J. Sci. Comput..

Discretisation of Global Attractors for Lattice Dynamical Systems

P. Kloeden, Xiaoying Han, S. Sonner, 2019, Journal of Dynamics and Differential Equations.

Discretisation of Global Attractors for Lattice Dynamical Systems

P. Kloeden, Xiaoying Han, S. Sonner, 2019, Journal of Dynamics and Differential Equations.

Comparison of Attractors of Asymptotically Equivalent Difference Equations

P. Kloeden, Hongyong Cui, 2017, Difference Equations, Discrete Dynamical Systems and Applications.

Pullback and forward dynamics of nonautonomous Laplacian lattice systems on weighted spaces

P. Kloeden, Xiaoying Han, 2021, Discrete & Continuous Dynamical Systems - S.

A nonlocal sample dependence SDE-PDE system modeling proton dynamics in a tumor

P. Kloeden, C. Surulescu, S. Sonner, 2016 .

The exponential integrator scheme for stochastic partial differential equations: Pathwise error bounds

Peter E. Kloeden, Andreas Neuenkirch, Tony Shardlow, 2011, J. Comput. Appl. Math..

Entropy Increase in Switching Systems

José María Amigó, Peter E. Kloeden, Ángel Giménez, 2013, Entropy.

On the uniqueness of solitary Rossby waves

P. Kloeden, 1987, The Journal of the Australian Mathematical Society. Series B. Applied Mathematics.

Coupled nonautonomous inclusion systems with spatially variable exponents

Peter E. Kloeden, Jacson Simsen, P. Kloeden, 2021 .

Equi-Attraction and The Continuous Dependence of Attractors on Time Delays

P. Kloeden, P. Rubio, 2008 .

EQUI-ATTRACTION AND THE CONTINUOUS DEPENDENCE OF ATTRACTORS ON PARAMETERS

P. Kloeden, L. Desheng, 2004, Glasgow Mathematical Journal.

Slower aging in women: a proposed evolutionary explanation.

P E Kloeden, O E Rossler, P. Kloeden, 1995, Bio Systems.

Weak solution of stochastic differential equations with fractional diffusion coefficient

P. Kloeden, Fuke Wu, Hao Yang, 2018 .

Comment on "Numerical methods for stochastic differential equations".

Kevin Burrage, Eckhard Platen, Pamela Burrage, 2006, Physical review. E, Statistical, nonlinear, and soft matter physics.

An Exponential Wagner-Platen Type Scheme for SPDEs

Sebastian Becker, Peter E. Kloeden, Arnulf Jentzen, 2013, SIAM J. Numer. Anal..

Time Discrete Approximation of Deterministic Differential Equations

P. Kloeden, E. Platen, 1992 .

A note on multistep methods and attracting sets of dynamical systems

Peter E. Kloeden, Jens Lorenz, P. Kloeden, 1989 .

Pullback attractors for non-autonomous quasi-linear parabolic equations with dynamical boundary conditions

P. Kloeden, Meihua Yang, Lu Yang, 2012 .

Stationary distribution of stochastic population dynamics with infinite delay

P. Kloeden, Fuke Wu, Hao Yang, 2022, Journal of Differential Equations.

The weak connectedness of the attainability set of weak solutions of the three-dimensional Navier–Stokes equations

P. Kloeden, J. Valero, José Valero, 2007, Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences.

The truncated Euler-Maruyama method for stochastic differential equations with Hölder diffusion coefficients

Xuerong Mao, Fuke Wu, Hao Yang, 2020, J. Comput. Appl. Math..

Maple for Stochastic Differential Equations

Lars Grüne, Peter E. Kloeden, Sasha Cyganowski, 2001 .

An Introduction to the Numerical Simulation of Stochastic Differential Equations

P. Kloeden, D. Higham, 2021 .

A predictive model for life expectancy curves.

O E Rössler, P E Kloeden, P. Kloeden, 1990, Bio Systems.

Switching systems and entropy

Peter E. Kloeden, Ángel Giménez, José M. Amigó, 2013 .

Constructing Permutations that Approximate Lebesgue Measure Preserving Dynamical Systems Under Spatial Discretization

P. Kloeden, J. Mustard, 1997 .

Numerical Modeling of Toroidal Dynamical Systems with Invariant Lebesgue Measure

Phil Diamond, Peter Kloeden, Alexei Pokrovskii, 1993, Complex Syst..

Exponential stability of the quasigeostrophic equation under random perturbations

P. Kloeden, Jinqiao Duan, B. Schmalfuß, 2004, math/0409212.

Dissipative Quasi-Geostrophic Motion under Temporally Almost Periodic Forcing☆☆☆

P. Kloeden, Jinqiao Duan, 1999, chao-dyn/9910004.

The dissipative quasigeostrophic equations

P. E. Kloeden, P. Kloeden, A. Bennett, 1981 .

An explicit example of Hopf bifurcation in fluid mechanics

P. Kloeden, R. Wells, 1983, Proceedings of the Royal Society of London. A. Mathematical and Physical Sciences.

Preference heterogeneity and its equilibrium path

Peter E. Kloeden, Ling Peng, P. Kloeden, 2021, Optimal Control Applications and Methods.

A solution method for heterogeneity involving present bias

Peter E. Kloeden, Ling Peng, P. Kloeden, 2020 .

A solution method for heterogeneity involving present bias

P. Kloeden, Ling Peng, 2020, Optimization and Engineering.

Time-consistent portfolio optimization

Peter E. Kloeden, Ling Peng, P. Kloeden, 2021, Eur. J. Oper. Res..

On the Fragmentary Complexity of Symbolic Sequences

Phil Diamond, Peter Kloeden, Victor S. Kozyakin, 1995, Theor. Comput. Sci..

THE UNIFORM ATTRACTOR OF A MULTI-VALUED PROCESS GENERATED BY REACTION-DIFFUSION DELAY EQUATIONS ON AN UNBOUNDED DOMAIN

P. Kloeden, Yejuan Wang, 2014 .

PULLBACK AND FORWARD ATTRACTORS FOR A DAMPED WAVE EQUATION WITH DELAYS

Peter E. Kloeden, Tomás Caraballo, P. Kloeden, 2004 .

Non-autonomous attractors for integro-differential evolution equations

P. Kloeden, T. Caraballo, 2009 .

Pullback attractors of reaction-diffusion inclusions with space-dependent delay

Peter E. Kloeden, P. Kloeden, Thomas Lorenz, 2017 .

The Envelope Attractor of Non-strict Multivalued Dynamical Systems with Application to the 3D Navier–Stokes and Reaction–Diffusion Equations

P. Kloeden, J. Valero, P. Marín-Rubio, 2013, Set-Valued and Variational Analysis.

The Envelope Attractor of Non-strict Multivalued Dynamical Systems with Application to the 3D Navier–Stokes and Reaction–Diffusion Equations

P. Kloeden, J. Valero, P. Marín-Rubio, 2013 .

Asymptotic behaviour of nonlocal reaction–diffusion equations

P. Kloeden, Thomas Lorenz, M. Anguiano, 2010 .

Numerical and finite delay approximations of attractors for logistic differential-integral equations with infinite delay

P. Kloeden, T. Caraballo, P. Marín-Rubio, 2007 .

Asymptotically autonomous multivalued Cauchy problems with spatially variable exponents

P. Kloeden, M. S. Simsen, J. Simsen, 2017 .

Global and pullback attractors of set-valued skew product flows

P. E. Kloeden, P. Kloeden, T. Caraballo, 2006 .

Pullback Attractors in Dissipative Nonautonomous Differential Equations Under Discretization

Peter E. Kloeden, David Cheban, P. Kloeden, 2001 .

MORSE SPECTRUM FOR NONAUTONOMOUS DIFFERENTIAL EQUATIONS

M. Rasmussen, P. Kloeden, F. Colonius, 2008 .

FOR NONAUTONOMOUS DIFFERENTIAL EQUATIONS

M. Rasmussen, P. Kloeden, F. Colonius, 2008 .

Discretization, Inflation and Perturbation of Attractors

L. Grüne, P. Kloeden, 2001 .

The inflation of nonautonomous systems and their pullback attractors

P. Kloeden, V. Kozyakin, J. Goethe, 2000 .

The periodic quasigeostrophic equations: existence and uniqueness of strong solutions

P. Kloeden, A. Bennett, 1982, Proceedings of the Royal Society of Edinburgh: Section A Mathematics.

Stochastic partial differential equations with additive noise on time-varying domains

P. Kloeden, J. Real, H. Crauel, 2010 .

Pullback attractors for a semilinear heat equation on time-varying domains ✩

Peter E. Kloeden, Chunyou Sun, P. Kloeden, 2009 .

Pullback attractors for a semilinear heat equation in a non-cylindrical domain

Peter E. Kloeden, Pedro Marín-Rubio, P. Kloeden, 2008 .

Long time behavior of stochastic parabolic problems with white noise in materials with thermal memory

P. Kloeden, T. Caraballo, Linfang Liu, 2017 .

Multi-step methods for random ODEs driven by Itô diffusions

Yusuke Asai, Peter E. Kloeden, P. Kloeden, 2016, J. Comput. Appl. Math..

Chemostats with random inputs and wall growth

Xiaoying Han, Peter E. Kloeden, Tomás Caraballo, 2015 .

Discretization of a Random Dynamical System near a Hyperbolic Point

P. Kloeden, L. Arnold, 2009 .

The persistence of synchronization under environmental noise

Peter E. Kloeden, Tomás Caraballo, P. Kloeden, 2005, Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences.

Pathwise Approximation of Random Ordinary Differential Equations

Lars Grüne, Peter E. Kloeden, L. Grüne, 2001 .

Attractors with higher-order regularity of stochastic reaction–diffusion equations on time-varying domains

P. Kloeden, Meihua Yang, Lu Yang, 2020 .

Long time behavior of stochastic parabolic problems with white noise in materials with thermal memory

P. Kloeden, T. Caraballo, Linfang Liu, 2017, Revista Matemática Complutense.

Stable Integration of Stiff Random Ordinary Differential Equations

Peter E. Kloeden, E. Herrmann, P. Kloeden, 2013 .

ASYMPTOTIC BEHAVIOUR OF RANDOM MARKOV CHAINS WITH TRIDIAGONAL GENERATORS

P. Kloeden, V. Kozyakin, 2012, Bulletin of the Australian Mathematical Society.

Synchronization of noisy dissipative systems under discretization

P. Kloeden, A. Neuenkirch, R. Pavani, 2009 .

The Pathwise Numerical Approximation of Stationary Solutions of Semilinear Stochastic Evolution Equations

Peter E. Kloeden, Tomás Caraballo, P. Kloeden, 2006 .

Dynamics of Zika Virus Epidemic in Random Environment

P. Kloeden, Xiaoying Han, Yusuke Asai, 2019, Studies in Systems, Decision and Control.

Higher order numerical schemes for a(cid:14)nely controlled nonlinear systems (cid:3)

P. Kloeden, F. Mathematik, L. Gr¨une, 2022 .

Pullback attractors of a multi-valued process generated by parabolic differential equations with unbounded delays

P. Kloeden, Yejuan Wang, 2013 .

Asymptotic behaviour of nonautonomous difference inclusions

Peter E. Kloeden, Björn Schmalfuss, P. Kloeden, 1998 .

Strong \begin{document}$ (L^2,L^\gamma\cap H_0^1) $\end{document}-continuity in initial data of nonlinear reaction-diffusion equation in any space dimension

P. Kloeden, Wenqiang Zhao, Hongyong Cui, 2020, Electronic Research Archive.

Local equi-attraction of pullback attractor sections

Peter E. Kloeden, Jie Xin, Fuzhi Li, 2021 .

Strong $(L^2,L^\gamma\cap H_0^1)$-continuity in initial data of nonlinear reaction-diffusion equation in any space dimension

P. Kloeden, Wenqiang Zhao, Hongyong Cui, 2019, 1905.07580.

Asymptotic Behavior of a Nonautonomous p-Laplacian Lattice System

Peter E. Kloeden, Anhui Gu, P. Kloeden, 2016, Int. J. Bifurc. Chaos.

Divergence of the multilevel Monte Carlo Euler method for nonlinear stochastic differential equations

Peter E. Kloeden, Arnulf Jentzen, Martin Hutzenthaler, 2011, 1105.0226.

Strong convergence of an explicit numerical method for SDEs with nonglobally Lipschitz continuous coefficients

P. Kloeden, Arnulf Jentzen, Martin Hutzenthaler, 2010, 1010.3756.

Basin of attraction of cycles of discretizations of dynamical systems with SRB invariant measures

P. Kloeden, P. Diamond, A. Pokrovskii, 1996 .

Statistical properties of discretizations of a class of chaotic dynamical systems

P. Kloeden, P. Diamond, M. Suzuki, 1996 .

Lower and upper bounds for strong approximation errors for numerical approximations of stochastic heat equations

Sebastian Becker, Peter E. Kloeden, Arnulf Jentzen, 2018, BIT Numerical Mathematics.

Ito Stochastic Calculus

P. Kloeden, E. Platen, 1992 .

Multilevel Monte Carlo for stochastic differential equations with additive fractional noise

Peter E. Kloeden, Andreas Neuenkirch, Raffaella Pavani, 2011, Ann. Oper. Res..

Asymptotic behaviour of a class of discontinuous difference equations

P. Kloeden, M. Fisher, 1978, The Journal of the Australian Mathematical Society. Series B. Applied Mathematics.

Digitization of nonautonomous control systems

P. Kloeden, R. Fabbri, Russell Johnson, 2003 .

On the computation of invariant measures in random dynamical systems

Peter E. Kloeden, Peter Imkeller, P. Kloeden, 2003 .

Numerical Solutions of Stochastic Differential Equations

P. Kloeden, E. Platen, 1995 .

Lyapunov Sequences and a Turnpike Theorem without Convexity

P. Kloeden, A. Rubinov, Z. Dzalilov, 1998 .

Monotonic dynamical systems under spatial discretization

P. Kloeden, P. Diamond, V. Kozyakin, 1998 .

Higher Order Approximate Markov Chain Filters

Peter E. Kloeden, Eckhard Platen, Henri Schurz, 1993 .

Topologies for general semidynamical systems

P. Kloeden, 1978 .

General control systems

Peter E. Kloeden, P. Kloeden, 1978 .

Pullback attractors for non-autonomous evolution equations with spatially variable exponents

P. Kloeden, J. Simsen, 2014 .

Comparative Properties of Three Metrics in the Space of Compact Convex Sets

Alexander Rubinov, Phil Diamond, Peter Kloeden, 1997 .

Probability Theory and Stochastic Processes

Eckhard Platen, Peter E. Kloeden, P. Kloeden, 1992 .

Selected Applications of Strong Approximations

P. Kloeden, E. Platen, 1992 .

Probability and Statistics

P. Kloeden, E. Platen, 1992 .

On effects of discretization on estimators of drift parameters for diffusion processes

Peter E. Kloeden, Michael Sørensen, Eckhard Platen, 1996, Journal of Applied Probability.

Stability and boundedness of solutions of Stieltjes Differential Equations

P. Kloeden, M. Gil', 2003 .

Maple Schemes for Jump-diiusion Stochastic Diierential Equations

P. Kloeden, 2007 .

MAPLE for Jump—Diffusion Stochastic Differential Equations in Finance

Lars Grüne, Peter E. Kloeden, Sasha Cyganowski, 2002 .

Numerical Schemes for Stochastic Differential Equation Models

P. Kloeden, D. Higham, 2008 .

THE NUMERICAL STABILITY OF STOCHASTIC ORDINARY DIFFERENTIAL EQUATIONS WITH ADDITIVE NOISE

Peter E. Kloeden, Evelyn Buckwar, P. Kloeden, 2011 .

MAPLE and MATLAB for stochastic differential equations in finance

Desmond J. Higham, Peter E. Kloeden, P. Kloeden, 2002 .

The quasi‐geostrophic equations: Approximation, predictability and equilibrium spectra of solutions

P. Kloeden, A. Bennett, 1981 .

Boundary Conditions for Limited-Area Forecasts

P. Kloeden, A. Bennett, 1978 .

Non-autonomous lattice systems with switching effects and delayed recovery

Xiaoying Han, Peter E. Kloeden, P. Kloeden, 2016 .

Well-posedness and regularity for solutions of caputo stochastic fractional differential equations in Lp spaces

Doan Thai Son, P. Kloeden, P. T. Huong, 2021, Stochastic Analysis and Applications.

Bernd Aulbach—Obituary

P. Kloeden, S. Siegmund, F. Colonius, 2006 .

Lyapunov exponents and rotation number of two-dimensional systems with telegraphic noise

Peter E. Kloeden, P. Kloeden, L. Arnold, 1989 .

Nonautonomous systems, cocycle attractors and variable time-step discretization

Peter E. Kloeden, Björn Schmalfuß, P. Kloeden, 1997, Numerical Algorithms.

Robustness of dynamical systems to a class of nonsmooth perturbations

P. Kloeden, M. Krasnosel’skiǐ, P. Diamond, 1996 .

On Sharkovsky's cycle coexistence ordering

P. Kloeden, 1979, Bulletin of the Australian Mathematical Society.