Ergodicity for functional stochastic differential equations and applications

J Bao, G Yin, C Yuan - Nonlinear Analysis: Theory, Methods & Applications, 2014 - Elsevier
In this paper, using the remote start or dissipative method, we investigate ergodicity for
several kinds of functional stochastic equations including functional stochastic differential …

[HTML][HTML] Jump type stochastic differential equations with non-Lipschitz coefficients: non-confluence, Feller and strong Feller properties, and exponential ergodicity

F Xi, C Zhu - Journal of Differential Equations, 2019 - Elsevier
This paper considers multidimensional jump type stochastic differential equations with super
linear and non-Lipschitz coefficients. After establishing a sufficient condition for …

Ergodicity of a Lévy-driven SDE arising from multiclass many-server queues

A Arapostathis, G Pang, N Sandrić - 2019 - projecteuclid.org
We study the ergodic properties of a class of multidimensional piecewise Ornstein–
Uhlenbeck processes with jumps, which contains the limit of the queueing processes arising …

[HTML][HTML] Coupling and exponential ergodicity for stochastic differential equations driven by Lévy processes

MB Majka - Stochastic processes and their applications, 2017 - Elsevier
We present a novel idea for a coupling of solutions of stochastic differential equations driven
by Lévy noise, inspired by some results from the optimal transportation theory. Then we use …

Exponential Ergodicity of Stochastic Burgers Equations Driven by α-Stable Processes

Z Dong, L Xu, X Zhang - Journal of Statistical Physics, 2014 - Springer
In this work, we prove the strong Feller property and the exponential ergodicity of stochastic
Burgers equations driven by α/2-subordinated cylindrical Brownian motions with α∈(1, 2) …

[图书][B] Asymptotic analysis for functional stochastic differential equations

J Bao, G Yin, C Yuan, G Yin - 2016 - Springer
The ergodicity of SDEs and SPDEs, in which the state spaces are independent of the past,
has been studied extensively. So far, there are several approaches to investigate ergodicity …

Transition density estimates for diagonal systems of SDEs driven by cylindrical -stable processes

T Kulczycki, M Ryznar - arXiv preprint arXiv:1711.07539, 2017 - arxiv.org
We consider the system of stochastic differential equation $ dX_t= A (X_ {t-})\, dZ_t $, $ X_0=
x $, driven by cylindrical $\alpha $-stable process $ Z_t $ in $\mathbb {R}^ d $. We assume …

[HTML][HTML] Ergodicity of the stochastic real Ginzburg–Landau equation driven by α-stable noises

L Xu - Stochastic Processes and their Applications, 2013 - Elsevier
We study the ergodicity of the stochastic real Ginzburg–Landau equation driven by additive
α-stable noises, showing that as α∈(3/2, 2), this stochastic system admits a unique invariant …

Asymptotic stability and cut-off phenomenon for the underdamped Langevin dynamics

S Lee, M Ramil, I Seo - arXiv preprint arXiv:2311.18263, 2023 - arxiv.org
In this article, we provide detailed analysis of the long-time behavior of the underdamped
Langevin dynamics. We first provide a necessary condition guaranteeing that the zero-noise …

Ergodicity for the 3D stochastic Navier–Stokes equations perturbed by Lévy noise

MT Mohan, K Sakthivel… - Mathematische …, 2019 - Wiley Online Library
In this work we construct a Markov family of martingale solutions for 3D stochastic Navier–
Stokes equations (SNSE) perturbed by Lévy noise with periodic boundary conditions. Using …