EXPONENTIAL MIXING FOR SOME SPDEs WITH LÉVY NOISE-Reference-Cited by-同舟云学术

EXPONENTIAL MIXING FOR SOME SPDEs WITH LÉVY NOISE

Published:2011-09 Issue:02n03 Volume:11 Page:521-534
ISSN:0219-4937
Container-title:Stochastics and Dynamics
language:en
Short-container-title:Stoch. Dyn.

Author:

PRIOLA ENRICO¹,XU LIHU²,ZABCZYK JERZY³

Affiliation:

1. Dipartimento di Matematica, Università di Torino, via Carlo Alberto 10, 10123, Torino, Italy

2. TU Berlin, Fakultät II, Institut für Mathematik, Strαβe des 17. Juni 136, D-10623 Berlin, Germany

3. Institute of Mathematics, Polish Academy of Sciences, ul. Sniadeckich 8, P-00-950 Warszawa, Poland

Abstract

We show how gradient estimates for transition semigroups can be used to establish exponential mixing for a class of Markov processes in infinite dimensions. We concentrate on semilinear systems driven by cylindrical α-stable noises introduced in [18], α ∈ (0,2). We first prove that if the nonlinearity is bounded, then the system is ergodic and strong mixing. Then we show that the system is exponentially mixing provided that the nonlinearity, or its Lipschitz constant, are sufficiently small.

Publisher

World Scientific Pub Co Pte Lt

Subject

Modelling and Simulation

Link

https://www.worldscientific.com/doi/pdf/10.1142/S0219493711003425

Reference20 articles.

1. Existence of mild solutions for stochastic differential equations and semilinear equations with non-Gaussian Lévy noise

2. Parabolic SPDEs driven by Poisson white noise

3. Time irregularity of generalized Ornstein–Uhlenbeck processes

4. A semigroup approach to Kolmogoroff equations in Hilbert spaces

Cited by 23 articles. 订阅此论文施引文献订阅此论文施引文献，注册后可以免费订阅5篇论文的施引文献，订阅后可以查看论文全部施引文献

1. Attractors. Then and now;Russian Mathematical Surveys;2023

2. Attractors. Then and now;Uspekhi Matematicheskikh Nauk;2023

3. Singular integrals of subordinators with applications to structural properties of SPDEs;Transactions of the American Mathematical Society;2022-06-30

4. On a class of stochastic partial differential equations with multiple invariant measures;Nonlinear Differential Equations and Applications NoDEA;2021-04-07

5. Ergodicity of Stochastic Hydrodynamical-Type Evolution Equations Driven by $$\alpha $$-Stable Noise;Contemporary Approaches and Methods in Fundamental Mathematics and Mechanics;2020-11-25