Random Splitting of Fluid Models: Unique Ergodicity and Convergence

[1]  Minh C. Tran,et al.  Theory of Trotter Error with Commutator Scaling , 2021 .

[2]  Arnaud Debussche,et al.  A Piecewise Deterministic Limit for a Multiscale Stochastic Spatial Gene Network , 2020, Applied Mathematics & Optimization.

[3]  Sean D Lawley,et al.  Extreme first passage times of piecewise deterministic Markov processes , 2019, Nonlinearity.

[4]  J. Bedrossian,et al.  Almost-sure enhanced dissipation and uniform-in-diffusivity exponential mixing for advection–diffusion by stochastic Navier–Stokes , 2019, Probability Theory and Related Fields.

[5]  Alain Durmus,et al.  Piecewise deterministic Markov processes and their invariant measures , 2018, Annales de l'Institut Henri Poincaré, Probabilités et Statistiques.

[6]  Yuan Su,et al.  Faster quantum simulation by randomization , 2018, Quantum.

[7]  Michel Benaim,et al.  A user-friendly condition for exponential ergodicity in randomly switched environments. , 2018, 1803.03456.

[8]  A. Shirikyan,et al.  Exponential mixing for a class of dissipative PDEs with bounded degenerate noise , 2018, Geometric and Functional Analysis.

[9]  G. Roberts,et al.  Ergodicity of the zigzag process , 2017, The Annals of Applied Probability.

[10]  Jonathan C. Mattingly,et al.  Smooth invariant densities for random switching on the torus , 2017, 1708.01390.

[11]  Shengqiang Liu,et al.  Threshold dynamics and ergodicity of an SIRS epidemic model with Markovian switching , 2017, 1707.06380.

[12]  Jonathan C. Mattingly,et al.  Stochastic Switching in Infinite Dimensions with Applications to Random Parabolic PDE , 2014, SIAM J. Math. Anal..

[13]  Jonathan C. Mattingly,et al.  Regularity of invariant densities for 1D systems with random switching , 2014, 1406.5425.

[14]  Jonathan C. Mattingly,et al.  Sensitivity to switching rates in stochastically switched odes , 2013, 1310.2525.

[15]  M. Benaim,et al.  Qualitative properties of certain piecewise deterministic Markov processes , 2012, 1204.4143.

[16]  David A. Cox.  Pure and Applied Mathematics: A Wiley Series of Texts, Monographs and Tracts , 2012 .

[17]  Tobias Hurth,et al.  Invariant densities for dynamical systems with random switching , 2012, 1203.5744.

[18]  Oswaldo Luiz V. Costa,et al.  Singular Perturbation for the Discounted Continuous Control of Piecewise Deterministic Markov Processes , 2010, 49th IEEE Conference on Decision and Control (CDC).

[19]  Syoiti Ninomiya,et al.  A new higher-order weak approximation scheme for stochastic differential equations and the Runge–Kutta method , 2009, Finance Stochastics.

[20]  Jonathan C. Mattingly,et al.  Yet Another Look at Harris’ Ergodic Theorem for Markov Chains , 2008, 0810.2777.

[21]  S. Ninomiya,et al.  Weak Approximation of Stochastic Differential Equations and Application to Derivative Pricing , 2006, math/0605361.

[22]  Jonathan C. Mattingly.  On recent progress for the stochastic Navier Stokes equations , 2004, math/0409194.

[23]  Jonathan C. Mattingly,et al.  Ergodicity of the 2D Navier-Stokes equations with degenerate stochastic forcing , 2004, math/0406087.

[24]  A. Shirikyan,et al.  Some limiting properties of randomly forced two-dimensional Navier–Stokes equations , 2003, Proceedings of the Royal Society of Edinburgh: Section A Mathematics.

[25]  G. Prato,et al.  Two-Dimensional Navier--Stokes Equations Driven by a Space--Time White Noise , 2002 .

[26]  Jonathan C. Mattingly,et al.  Ergodicity for SDEs and approximations: locally Lipschitz vector fields and degenerate noise , 2002 .

[27]  John M. Lee.  Introduction to Smooth Manifolds , 2002 .

[28]  Weinan E,et al.  Gibbsian Dynamics and Ergodicity¶for the Stochastically Forced Navier–Stokes Equation , 2001 .

[29]  Jonathan C. Mattingly,et al.  Ergodicity for the Navier‐Stokes equation with degenerate random forcing: Finite‐dimensional approximation , 2001 .

[30]  A. Shirikyan,et al.  Stochastic Dissipative PDE's and Gibbs Measures , 2000 .

[31]  David L. Elliott,et al.  Geometric control theory , 2000, IEEE Trans. Autom. Control..

[32]  A. Arnold,et al.  An Operator Splitting Method for the Wigner--Poisson Problem , 1996 .

[33]  Tasso J. Kaper,et al.  N th-order operator splitting schemes and nonreversible systems , 1996 .

[34]  Franco Flandoli,et al.  Ergodicity of the 2-D Navier-Stokes equation under random perturbations , 1995 .

[35]  M. Bernhard.  Introduction to Chaotic Dynamical Systems , 1992 .

[36]  R. Devaney.  An Introduction to Chaotic Dynamical Systems , 1990 .

[37]  A. McNabb.  Comparison theorems for differential equations , 1986 .

[38]  E. Nummelin.  The discrete skeleton method and a total variation limit theorem for continous-time Markov processes. , 1978 .

[39]  H. Sussmann.  Orbits of families of vector fields and integrability of distributions , 1973 .

[40]  T. Nagano.  Linear differential systems with singularities and an application to transitive Lie algebras , 1966 .

[41]  B. Williamson.  On SDEs with Partial Damping Inspired by the Navier-Stokes Equations , 2019 .

[42]  Pierre Monmarché.  On H 1 and entropic convergence for contractive PDMP , 2015 .

[43]  G. Strang,et al.  Operator splitting , 2011 .

[44]  M. Nikolenko,et al.  Translated from Russian by , 2008 .

[45]  Malliavin Calculus,et al.  Approximation of Expectation of Diffusion Processes based on Lie Algebra and Malliavin Calculus , 2003 .

[46]  A. Mondino.  to Riemannian manifolds , 1999 .

[47]  J. Zukas.  Introduction to the Modern Theory of Dynamical Systems , 1998 .

[48]  John M. Lee.  Riemannian Manifolds: An Introduction to Curvature , 1997 .

[49]  Richard L. Tweedie,et al.  Markov Chains and Stochastic Stability , 1993, Communications and Control Engineering Series.

[50]  Y. Kifer.  Ergodic theory of random transformations , 1986 .

[51]  M. Freidlin,et al.  Random Perturbations of Dynamical Systems , 1984 .

[52]  I. I. Gikhman.  Convergence to Markov processes , 1969 .