Arnulf Jentzen

发表

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.

A random Euler scheme for Carathéodory differential equations

Arnulf Jentzen, A. Neuenkirch, 2009 .

N A ] 1 0 A ug 2 01 7 On multilevel Picard numerical approximations for high-dimensional nonlinear parabolic partial differential equations and high-dimensional nonlinear backward stochastic differential equations

E. Weinan, M. Hutzenthaler, Arnulf Jentzen, 2018 .

N A ] 2 8 A ug 2 01 9 Deep neural network approximations for Monte Carlo algorithms

P. Grohs, Arnulf Jentzen, Diyora Salimova, 2019 .

Strong convergence rates and temporal regularity for Cox-Ingersoll-Ross processes and Bessel processes with accessible boundaries

M. Hutzenthaler, Arnulf Jentzen, Marco Noll, 2014, 1403.6385.

Numerical Approximations of Stochastic Differential Equations With Non-globally Lipschitz Continuous Coefficients

M. Hutzenthaler, Arnulf Jentzen, Martin Hutzenthaler, 2012, 1203.5809.

Local Lipschitz continuity in the initial value and strong completeness for nonlinear stochastic differential equations

M. Hutzenthaler, Arnulf Jentzen, S. Cox, 2013, 1309.5595.

A Milstein Scheme for SPDEs

Arnulf Jentzen, M. Röckner, 2010, Foundations of Computational Mathematics.

A mild Itô formula for SPDEs

G. Prato, Arnulf Jentzen, M. Roeckner, 2010, Transactions of the American Mathematical Society.

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.

Pathwise Numerical Approximations of SPDEs with Additive Noise under Non-global Lipschitz Coefficients

Arnulf Jentzen, 2009 .

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

P. Kloeden, Arnulf Jentzen, 2009, 1010.0161.

Strong and weak divergence of exponential and linear-implicit Euler approximations for stochastic partial differential equations with superlinearly growing nonlinearities

M. Hutzenthaler, Arnulf Jentzen, Diyora Salimova, 2019, 1903.06066.

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.

Strong convergence rates for nonlinearity-truncated Euler-type approximations of stochastic Ginzburg–Landau equations

Arnulf Jentzen, S. Becker, 2016, Stochastic Processes and their Applications.

Taylor Approximations for Stochastic Partial Differential Equations

P. Kloeden, Arnulf Jentzen, 2011 .

Strong convergence for explicit space–time discrete numerical approximation methods for stochastic Burgers equations

Arnulf Jentzen, Diyora Salimova, Timo Welti, 2017, Journal of Mathematical Analysis and Applications.

On a perturbation theory and on strong convergence rates for stochastic ordinary and partial differential equations with non-globally monotone coefficients

M. Hutzenthaler, Arnulf Jentzen, Martin Hutzenthaler, 2014, 1401.0295.

Exponential moments for numerical approximations of stochastic partial differential equations

Arnulf Jentzen, Primoz Pusnik, Primož Pušnik, 2016, Stochastics and Partial Differential Equations: Analysis and Computations.

On a perturbation theory and on strong convergence rates for stochastic ordinary and partial differential equations with nonglobally monotone coefficients

M. Hutzenthaler, Arnulf Jentzen, 2020 .

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 .

Overcoming the curse of dimensionality in the approximative pricing of financial derivatives with default risks

Philippe von Wurstemberger, M. Hutzenthaler, Arnulf Jentzen, 2019, Electronic Journal of Probability.

DNN Expression Rate Analysis of High-Dimensional PDEs: Application to Option Pricing

Arnulf Jentzen, Philipp Grohs, Christoph Schwab, 2018, Constructive Approximation.

On the differentiability of solutions of stochastic evolution equations with respect to their initial values

Arnulf Jentzen, R. Kurniawan, Timo Welti, 2016, 1611.00856.

Loss of regularity for Kolmogorov equations

Martin Hairer, Arnulf Jentzen, Martin Hutzenthaler, 2012, 1209.6035.

On stochastic differential equations with arbitrary slow convergence rates for strong approximation

Arnulf Jentzen, Thomas Muller-Gronbach, L. Yaroslavtseva, 2015, 1506.02828.

Counterexamples to local Lipschitz and local Hölder continuity with respect to the initial values for additive noise driven stochastic differential equations with smooth drift coefficient functions with at most polynomially growing derivatives

Arnulf Jentzen, Thomas Muller-Gronbach, L. Yaroslavtseva, 2020, Discrete & Continuous Dynamical Systems - B.

On the strong regularity of degenerate additive noise driven stochastic differential equations with respect to their initial values

Arnulf Jentzen, Thomas Muller-Gronbach, L. Yaroslavtseva, 2019, 1904.05963.

Strong convergence of full-discrete nonlinearity-truncated accelerated exponential Euler-type approximations for stochastic Kuramoto-Sivashinsky equations

Arnulf Jentzen, Martin Hutzenthaler, Diyora Salimova, 2016, 1604.02053.

Existence, uniqueness, and regularity for stochastic evolution equations with irregular initial values

Arnulf Jentzen, Ryan Kurniawan, Adam Andersson, 2014, Journal of Mathematical Analysis and Applications.

Multilevel Picard iterations for solving smooth semilinear parabolic heat equations

W. E, M. Hutzenthaler, Arnulf Jentzen, 2016, Partial Differential Equations and Applications.

Deep splitting method for parabolic PDEs

Patrick Cheridito, Arnulf Jentzen, C. Beck, 2019, SIAM J. Sci. Comput..

Regularity Properties for Solutions of Infinite Dimensional Kolmogorov Equations in Hilbert Spaces

Arnulf Jentzen, M. Hefter, R. Kurniawan, 2016, 1611.00858.

Weak convergence rates for temporal numerical approximations of stochastic wave equations with multiplicative noise

Arnulf Jentzen, S. Cox, F. Lindner, 2019, 1901.05535.

Taylor expansions of solutions of stochastic partial differential equations

Arnulf Jentzen, 2009, 0904.2232.

Workshop on Mathematics of Deep Learning

Arnulf Jentzen, C. Schwab, 2017 .

On the It\^o-Alekseev-Gr\"obner formula for stochastic differential equations

M. Hutzenthaler, Arnulf Jentzen, Sara Mazzonetto, 2018, 1812.09857.

Deep learning approximations for non-local nonlinear PDEs with Neumann boundary conditions

Arnulf Jentzen, L. Pellissier, S. Becker, 2022, Partial Differential Equations and Applications.

Normalized gradient flow optimization in the training of ReLU artificial neural networks

Arnulf Jentzen, G. Weiss, Simon Eberle, 2022, ArXiv.

Landscape Analysis for Shallow Neural Networks: Complete Classification of Critical Points for Affine Target Functions

Patrick Cheridito, Arnulf Jentzen, Florian Rossmannek, 2021, Journal of Nonlinear Science.

Convergence in Hölder norms with applications to Monte Carlo methods in infinite dimensions

M. Hutzenthaler, Arnulf Jentzen, S. Cox, 2016, IMA Journal of Numerical Analysis.

A proof of convergence for stochastic gradient descent in the training of artificial neural networks with ReLU activation for constant target functions

Arnulf Jentzen, Adrian Riekert, 2021, Zeitschrift für angewandte Mathematik und Physik.

Gradient descent provably escapes saddle points in the training of shallow ReLU networks

Patrick Cheridito, Arnulf Jentzen, Florian Rossmannek, 2022, ArXiv.

Algorithms for solving high dimensional PDEs: from nonlinear Monte Carlo to machine learning

Arnulf Jentzen, Weinan E, Jiequn Han, 2020, Nonlinearity.

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

M. Hutzenthaler, Arnulf Jentzen, Peter, 2010 .

Convergence analysis for gradient flows in the training of artificial neural networks with ReLU activation

Arnulf Jentzen, Adrian Riekert, 2021, Journal of Mathematical Analysis and Applications.

An efficient Monte Carlo scheme for Zakai equations

Patrick Cheridito, Arnulf Jentzen, C. Beck, 2022, ArXiv.

Machine Learning Approximation Algorithms for High-Dimensional Fully Nonlinear Partial Differential Equations and Second-order Backward Stochastic Differential Equations

W. E, Arnulf Jentzen, C. Beck, 2019, Journal of Nonlinear Science.

On arbitrarily slow convergence rates for strong numerical approximations of Cox–Ingersoll–Ross processes and squared Bessel processes

Arnulf Jentzen, M. Hefter, 2018, Finance and Stochastics.

DNN Expression Rate Analysis of High-Dimensional PDEs: Application to Option Pricing

P. Grohs, Arnulf Jentzen, C. Schwab, 2021, Constructive Approximation.

A Milstein Scheme for SPDEs

Arnulf Jentzen, M. Röckner, 2015, Foundations of Computational Mathematics.

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.

A proof of convergence for the gradient descent optimization method with random initializations in the training of neural networks with ReLU activation for piecewise linear target functions

Arnulf Jentzen, Adrian Riekert, 2021, J. Mach. Learn. Res..

On Multilevel Picard Numerical Approximations for High-Dimensional Nonlinear Parabolic Partial Differential Equations and High-Dimensional Nonlinear Backward Stochastic Differential Equations

W. E, M. Hutzenthaler, Arnulf Jentzen, 2019, Journal of Scientific Computing.

On full history recursive multilevel Picard approximations and numerical approximations of high-dimensional nonlinear parabolic partial differential equations

E. Weinan, M. Hutzenthaler, Arnulf Jentzen, 2016 .

Regularity Properties for Solutions of Infinite Dimensional Kolmogorov Equations in Hilbert Spaces

Arnulf Jentzen, M. Hefter, R. Kurniawan, 2018, Potential Analysis.

Weak convergence rates for numerical approximations of stochastic partial differential equations with nonlinear diffusion coefficients in UMD Banach spaces

Arnulf Jentzen, M. Hefter, R. Kurniawan, 2016, 1612.03209.

Efficient Approximation of High-Dimensional Functions With Neural Networks

Arnulf Jentzen, Patrick Cheridito, Florian Rossmannek, 2019, IEEE Transactions on Neural Networks and Learning Systems.

Full error analysis for the training of deep neural networks

Arnulf Jentzen, C. Beck, B. Kuckuck, 2019, Infinite Dimensional Analysis, Quantum Probability and Related Topics.

Lower bounds for artificial neural network approximations: A proof that shallow neural networks fail to overcome the curse of dimensionality

P. Grohs, Arnulf Jentzen, Sarah Koppensteiner, 2021, J. Complex..

Solving high-dimensional optimal stopping problems using deep learning pdf

Sebastian Becker, Arnulf Jentzen, Patrick Cheridito, 2019, European Journal of Applied Mathematics.

A proof that deep artificial neural networks overcome the curse of dimensionality in the numerical approximation of Kolmogorov partial differential equations with constant diffusion and nonlinear drift coefficients pdf

Arnulf Jentzen, Diyora Salimova, Timo Welti, 2018, Communications in Mathematical Sciences.

Strong overall error analysis for the training of artificial neural networks via random initializations pdf

Arnulf Jentzen, Adrian Riekert, Arnulf Jentzen, 2020, ArXiv.

Overall error analysis for the training of deep neural networks via stochastic gradient descent with random initialisation pdf

Arnulf Jentzen, Timo Welti, Arnulf Jentzen, 2020, Appl. Math. Comput..

Analysis of the generalization error: Empirical risk minimization over deep artificial neural networks overcomes the curse of dimensionality in the numerical approximation of Black-Scholes partial differential equations

Arnulf Jentzen, Philipp Grohs, Julius Berner, 2018, SIAM J. Math. Data Sci..

Efficient approximation of high-dimensional functions with deep neural networks pdf

Arnulf Jentzen, Patrick Cheridito, Florian Rossmannek, 2019, ArXiv.

Machine Learning Approximation Algorithms for High-Dimensional Fully Nonlinear Partial Differential Equations and Second-order Backward Stochastic Differential Equations

E Weinan, Arnulf Jentzen, Christian Beck, 2017, J. Nonlinear Sci..

A proof that artificial neural networks overcome the curse of dimensionality in the numerical approximation of Black-Scholes partial differential equations pdf

Arnulf Jentzen, Philippe von Wurstemberger, Philipp Grohs, 2018, Memoirs of the American Mathematical Society.

Non-convergence of stochastic gradient descent in the training of deep neural networks pdf

Arnulf Jentzen, Patrick Cheridito, Florian Rossmannek, 2020, J. Complex..

Convergence proof for stochastic gradient descent in the training of deep neural networks with ReLU activation for constant target functions pdf

Luca Scarpa, Arnulf Jentzen, Martin Hutzenthaler, 2021, ArXiv.

Deep learning based numerical approximation algorithms for stochastic partial differential equations and high-dimensional nonlinear filtering problems

Patrick Cheridito, Arnulf Jentzen, C. Beck, 2020, ArXiv.

Exponential moments for numerical approximations of stochastic partial differential equations

Arnulf Jentzen, Primož Pušnik, 2018, Stochastics and Partial Differential Equations: Analysis and Computations.

On the mild Itô formula in Banach spaces

Arnulf Jentzen, Sonja Cox, Ryan Kurniawan, 2016, 1612.03210.

Pricing and Hedging American-Style Options with Deep Learning

Arnulf Jentzen, Patrick Cheridito, Sebastian Becker, 2019, Journal of Risk and Financial Management.

Deep Optimal Stopping

Sebastian Becker, Arnulf Jentzen, Patrick Cheridito, 2018, J. Mach. Learn. Res..

Learning the random variables in Monte Carlo simulations with stochastic gradient descent: Machine learning for parametric PDEs and financial derivative pricing

Philippe von Wurstemberger, Arnulf Jentzen, S. Becker, 2022, ArXiv.

Solving high-dimensional partial differential equations using deep learning

Arnulf Jentzen, Weinan E, Jiequn Han, 2017, Proceedings of the National Academy of Sciences.

Algorithms for solving high dimensional PDEs: from nonlinear Monte Carlo to machine learning pdf

E Weinan, Arnulf Jentzen, Jiequn Han, 2020, Nonlinearity.

Overcoming the Curse of Dimensionality in the Numerical Approximation of Parabolic Partial Differential Equations with Gradient-Dependent Nonlinearities pdf

Arnulf Jentzen, Thomas Kruse, Martin Hutzenthaler, 2019, Foundations of Computational Mathematics.

Algorithmically Designed Artificial Neural Networks (ADANNs): Higher order deep operator learning for parametric partial differential equations

Philippe von Wurstemberger, Arnulf Jentzen, Adrian Riekert, 2023, ArXiv.

An overview on deep learning-based approximation methods for partial differential equations

M. Hutzenthaler, Arnulf Jentzen, C. Beck, 2020, Discrete and Continuous Dynamical Systems - B.

Overcoming the curse of dimensionality in the numerical approximation of semilinear parabolic partial differential equations

Arnulf Jentzen, Thomas Kruse, Martin Hutzenthaler, 2018, Proceedings of the Royal Society A.

On Multilevel Picard Numerical Approximations for High-Dimensional Nonlinear Parabolic Partial Differential Equations and High-Dimensional Nonlinear Backward Stochastic Differential Equations

E Weinan, Arnulf Jentzen, Thomas Kruse, 2017, Journal of Scientific Computing.

Weak Convergence Rates for Spatial Spectral Galerkin Approximations of Semilinear Stochastic Wave Equations with Multiplicative Noise

Arnulf Jentzen, Timo Welti, Ladislas Jacobe de Naurois, 2015, Applied Mathematics & Optimization.

Weak Convergence Rates for Euler-Type Approximations of Semilinear Stochastic Evolution Equations with Nonlinear Diffusion Coefficients

Arnulf Jentzen, Ryan Kurniawan, Arnulf Jentzen, 2015, Found. Comput. Math..

Weak convergence rates of spectral Galerkin approximations for SPDEs with nonlinear diffusion coefficients

Arnulf Jentzen, Daniel Conus, Ryan Kurniawan, 2014, The Annals of Applied Probability.

Analysis and Numerical Approximations

Arnulf Jentzen, Arnulf Jentzen, 2015 .

Lower error bounds for the stochastic gradient descent optimization algorithm: Sharp convergence rates for slowly and fast decaying learning rates

Arnulf Jentzen, Philippe von Wurstemberger, Arnulf Jentzen, 2018, J. Complex..

Exponential integrability properties of numerical approximation processes for nonlinear stochastic differential equations

Xiaojie Wang, Arnulf Jentzen, Martin Hutzenthaler, 2013, Math. Comput..

Deep Learning-Based Numerical Methods for High-Dimensional Parabolic Partial Differential Equations and Backward Stochastic Differential Equations

E Weinan, Arnulf Jentzen, Jiequn Han, 2017, Communications in Mathematics and Statistics.

On full history recursive multilevel Picard approximations and numerical approximations for high-dimensional nonlinear parabolic partial differential equations and high-dimensional nonlinear backward stochastic differential equations

E Weinan, Arnulf Jentzen, Thomas Kruse, 2016 .

Linear scaling algorithms for solving high-dimensional nonlinear parabolic differential equations

E. Weinan, M. Hutzenthaler, Arnulf Jentzen, 2016 .

Convergence rates for the stochastic gradient descent method for non-convex objective functions pdf

Arnulf Jentzen, Benjamin J. Fehrman, Benjamin Gess, 2019, J. Mach. Learn. Res..

Generalised multilevel Picard approximations pdf

Arnulf Jentzen, Michael B. Giles, Timo Welti, 2019, ArXiv.

A proof that rectified deep neural networks overcome the curse of dimensionality in the numerical approximation of semilinear heat equations

Tuan Anh Nguyen, Arnulf Jentzen, Thomas Kruse, 2019, SN Partial Differential Equations and Applications.

Strong error analysis for stochastic gradient descent optimization algorithms

Philippe von Wurstemberger, Arnulf Jentzen, B. Kuckuck, 2018, 1801.09324.

Pathwise Taylor schemes for random ordinary differential equations

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

Deep splitting method for parabolic PDEs pdf

Arnulf Jentzen, Patrick Cheridito, Christian Beck, 2019, SIAM J. Sci. Comput..

Nonlinear Monte Carlo methods with polynomial runtime for high-dimensional iterated nested expectations pdf

Arnulf Jentzen, Thomas Kruse, Christian Beck, 2020, ArXiv.

A Milstein Scheme for SPDEs

Arnulf Jentzen, Michael Röckner, Arnulf Jentzen, 2010, Found. Comput. Math..

Galerkin Approximations for the Stochastic Burgers Equation

Arnulf Jentzen, Dirk Blömker, Arnulf Jentzen, 2013, SIAM J. Numer. Anal..

Efficient simulation of nonlinear parabolic SPDEs with additive noise

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

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.

Existence, uniqueness, and convergence rates for gradient flows in the training of artificial neural networks with ReLU activation

Arnulf Jentzen, G. Weiss, Simon Eberle, 2021, Electronic Research Archive.

Solving stochastic differential equations and Kolmogorov equations by means of deep learning pdf

Sebastian Becker, Arnulf Jentzen, Philipp Grohs, 2018, ArXiv.

On arbitrarily slow convergence rates for strong numerical approximations of Cox–Ingersoll–Ross processes and squared Bessel processes

Arnulf Jentzen, Mario Hefter, Arnulf Jentzen, 2017, Finance Stochastics.

Nonlinear Monte Carlo methods with polynomial runtime for Bellman equations of discrete time high-dimensional stochastic optimal control problems

Arnulf Jentzen, C. Beck, T. Kruse, 2023, 2303.03390.

On the existence of minimizers in shallow residual ReLU neural network optimization landscapes

S. Dereich, Arnulf Jentzen, Sebastian Kassing, 2023, ArXiv.

Higher Order Pathwise Numerical Approximations of SPDEs with Additive Noise

Arnulf Jentzen, Arnulf Jentzen, 2011, SIAM J. Numer. Anal..

Overcoming the curse of dimensionality in the numerical approximation of backward stochastic differential equations pdf

Arnulf Jentzen, Thomas Kruse, Martin Hutzenthaler, 2021, J. Num. Math..

A proof of convergence for gradient descent in the training of artificial neural networks for constant target functions pdf

Arnulf Jentzen, Patrick Cheridito, Florian Rossmannek, 2021, J. Complex..

Renormalized powers of Ornstein-Uhlenbeck processes and well-posedness of stochastic Ginzburg-Landau equations

E. Weinan, Arnulf Jentzen, Hao Shen, 2013, 1302.5930.

Lower bounds for weak approximation errors for spatial spectral Galerkin approximations of stochastic wave equations

Arnulf Jentzen, Ladislas Jacobe de Naurois, Timo Welti, 2016, 1701.04351.

An Exponential Wagner-Platen Type Scheme for SPDEs

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

A Break of the Complexity of the Numerical Approximation of Nonlinear SPDEs with Multiplicative Noise

Arnulf Jentzen, M. Roeckner, 2010 .

On existence and uniqueness properties for solutions of stochastic fixed point equations

Arnulf Jentzen, Lukas Gonon, Martin Hutzenthaler, 2019, Discrete & Continuous Dynamical Systems - B.

Convergence rates for gradient descent in the training of overparameterized artificial neural networks with biases pdf

Arnulf Jentzen, Timo Kröger, Arnulf Jentzen, 2021, ArXiv.

On the existence of global minima and convergence analyses for gradient descent methods in the training of deep neural networks pdf

Arnulf Jentzen, Adrian Riekert, Arnulf Jentzen, 2021, ArXiv.

Strong Overall Error Analysis for the Training of Artificial Neural Networks Via Random Initializations

Arnulf Jentzen, Adrian Riekert, 2020, Communications in Mathematics and Statistics.

Weak error analysis for stochastic gradient descent optimization algorithms

Arnulf Jentzen, Diyora Salimova, L. Gonon, 2020, ArXiv.

Convergence proof for stochastic gradient descent in the training of deep neural networks with ReLU activation for constant target functions

M. Hutzenthaler, Arnulf Jentzen, Luca Scarpa, 2021, ArXiv.

Learning the random variables in Monte Carlo simulations with stochastic gradient descent: Machine learning for parametric PDEs and financial derivative pricing

Philippe von Wurstemberger, Arnulf Jentzen, S. Becker, 2022, Mathematical Finance.

Deep neural network approximations for Monte Carlo algorithms pdf

Arnulf Jentzen, Philipp Grohs, Diyora Salimova, 2019, ArXiv.

Space-time error estimates for deep neural network approximations for differential equations pdf

Arnulf Jentzen, Philipp Grohs, Fabian Hornung, 2019, Advances in Computational Mathematics.

Towards a regularity theory for ReLU networks – chain rule and global error estimates

Arnulf Jentzen, Philipp Grohs, Julius Berner, 2019, 2019 13th International conference on Sampling Theory and Applications (SampTA).

Convergence of the Stochastic Euler Scheme for Locally Lipschitz Coefficients

Arnulf Jentzen, Martin Hutzenthaler, M. Hutzenthaler, 2009, Found. Comput. Math..

Multilevel Picard approximations for high-dimensional semilinear second-order PDEs with Lipschitz nonlinearities pdf

Tuan Anh Nguyen, Arnulf Jentzen, Martin Hutzenthaler, 2020, ArXiv.

Space-time deep neural network approximations for high-dimensional partial differential equations pdf

Arnulf Jentzen, Fabian Hornung, Diyora Salimova, 2020, ArXiv.

Numerical simulations for full history recursive multilevel Picard approximations for systems of high-dimensional partial differential equations

Philippe von Wurstemberger, M. Hutzenthaler, Arnulf Jentzen, 2020, Communications in Computational Physics.

Overcoming the curse of dimensionality in the numerical approximation of high-dimensional semilinear elliptic partial differential equations pdf

Arnulf Jentzen, Lukas Gonon, Christian Beck, 2020, ArXiv.

Uniform error estimates for artificial neural network approximations for heat equations

P. Grohs, Arnulf Jentzen, D. Šiška, 2019, IMA Journal of Numerical Analysis.

Solving the Kolmogorov PDE by Means of Deep Learning

Arnulf Jentzen, Philipp Grohs, Nor Jaafari, 2018, Journal of Scientific Computing.

Strong convergence rates for an explicit numerical approximation method for stochastic evolution equations with non-globally Lipschitz continuous nonlinearities

Arnulf Jentzen, Arnulf Jentzen, Primovz Puvsnik, 2015, IMA Journal of Numerical Analysis.

An efficient Monte Carlo scheme for Zakai equations

Patrick Cheridito, Arnulf Jentzen, C. Beck, 2022, Commun. Nonlinear Sci. Numer. Simul..

On nonlinear Feynman–Kac formulas for viscosity solutions of semilinear parabolic partial differential equations

Arnulf Jentzen, Martin Hutzenthaler, Christian Beck, 2020, Stochastics and Dynamics.

Overcoming the curse of dimensionality: Solving high-dimensional partial differential equations using deep learning pdf

E Weinan, Arnulf Jentzen, Jiequn Han, 2017, ArXiv.

1 A mild Itô formula for SPDEs

G. Prato, Arnulf Jentzen, M. Röckner, 2010 .

Overcoming the curse of dimensionality in the numerical approximation of Allen–Cahn partial differential equations via truncated full-history recursive multilevel Picard approximations

Arnulf Jentzen, Thomas Kruse, Christian Beck, 2019, J. Num. Math..

On the Alekseev-Gröbner formula in Banach spaces

Arnulf Jentzen, F. Lindner, Primovz Puvsnik, 2018, Discrete & Continuous Dynamical Systems - B.

A proof that rectified deep neural networks overcome the curse of dimensionality in the numerical approximation of semilinear heat equations

Arnulf Jentzen, T. Kruse, T. Nguyen, 2019, SN Partial Differential Equations and Applications.

N A ] 1 1 A pr 2 01 3 GALERKIN APPROXIMATIONS FOR THE STOCHASTIC BURGERS EQUATION

Arnulf Jentzen, D. Blömker, 2021 .

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.

Strong convergence rates on the whole probability space for space-time discrete numerical approximation schemes for stochastic Burgers equations

Arnulf Jentzen, F. Lindner, Primož Pušnik, 2019, ArXiv.

Exponential moment bounds and strong convergence rates for tamed-truncated numerical approximations of stochastic convolutions

Arnulf Jentzen, Felix Lindner, Primoz Pusnik, 2018, Numerical Algorithms.

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.

On stochastic differential equations with arbitrarily slow convergence rates for strong approximation in two space dimensions

Arnulf Jentzen, Máté Gerencsér, Diyora Salimova, 2017, Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences.

On stochastic differential equations with arbitrary slow convergence rates for strong approximation

Arnulf Jentzen, Thomas Muller-Gronbach, L. Yaroslavtseva, 2015, 1506.02828.

Non-globally Lipschitz Counterexamples for the stochastic Euler scheme

Arnulf Jentzen, Martin Hutzenthaler, 2009 .

Taylor expansions of solutions of stochastic partial differential equations

Arnulf Jentzen, 2009, 0904.2232.

Weak Convergence Rates for Euler-Type Approximations of Semilinear Stochastic Evolution Equations with Nonlinear Diffusion Coefficients

Arnulf Jentzen, R. Kurniawan, 2020, Foundations of Computational Mathematics.

Journal of Mathematical Analysis and Applications

V. G. Troitsky, P. L. Combettes, L. Henlein, 1960 .

Full error analysis for the training of deep neural networks

Arnulf Jentzen, C. Beck, Benno Kuckuck, 2019, Infinite Dimensional Analysis, Quantum Probability and Related Topics.

Full history recursive multilevel Picard approximations for ordinary differential equations with expectations pdf

Arnulf Jentzen, Martin Hutzenthaler, Christian Beck, 2021, ArXiv.