Limit theorems in Wasserstein distance for empirical measures of diffusion processes on Riemannian manifolds

FY Wang, JX Zhu - Annales de l'Institut Henri Poincare (B) …, 2023 - projecteuclid.org
Let (M, ρ) be a connected compact Riemannian manifold without boundary or with a convex
boundary∂ M, let V∈ C 2 (M) such that μ (dx):= e V (x) dx is a probability measure, where …

[HTML][HTML] Central limit theorem for Markov processes with spectral gap in the Wasserstein metric

T Komorowski, A Walczuk - Stochastic Processes and their Applications, 2012 - Elsevier
Suppose that {Xt, t≥ 0} is a non-stationary Markov process, taking values in a Polish metric
space E. We prove the law of large numbers and central limit theorem for an additive …

[HTML][HTML] Ergodic and mixing properties of the Boussinesq equations with a degenerate random forcing

J Földes, N Glatt-Holtz, G Richards… - Journal of Functional …, 2015 - Elsevier
We establish the existence, uniqueness and attraction properties of an ergodic invariant
measure for the Boussinesq equations in the presence of a degenerate stochastic forcing …

Statistical properties of 2D stochastic Navier-Stokes equations with time-periodic forcing and degenerate stochastic forcing

R Liu, K Lu - arXiv preprint arXiv:2105.00598, 2021 - arxiv.org
We consider the incompressible 2D Navier-Stokes equations with periodic boundary
conditions driven by a deterministic time periodic forcing and a degenerate stochastic …

Limit theorems for additive functionals of stochastic functional differential equations with infinite delay

Y Wang, F Wu, C Zhu - Journal of Differential Equations, 2022 - Elsevier
This paper examines limit theorems for a class of stochastic functional differential equations
with infinite delay. Under non-Lipschitz conditions, the strong law of large numbers and the …

Exponential mixing and limit theorems of quasi-periodically forced 2D stochastic Navier-Stokes Equations in the hypoelliptic setting

R Liu, K Lu - arXiv preprint arXiv:2205.14348, 2022 - arxiv.org
We consider the incompressible 2D Navier-Stokes equations on the torus driven by a
deterministic time quasi-periodic force and a noise that is white in time and extremely …

Exponential mixing for random nonlinear wave equations: weak dissipation and localized control

Z Liu, D Wei, S Xiang, Z Zhang, JC Zhao - arXiv preprint arXiv:2407.15058, 2024 - arxiv.org
We establish a new criterion for exponential mixing of random dynamical systems. Our
criterion is applicable to a wide range of systems, including in particular dispersive …

Ergodicity of regime-switching functional diffusions with infinite delay and application to a numerical algorithm for stochastic optimization

B Shi, Y Wang, F Wu - SIAM Journal on Control and Optimization, 2022 - SIAM
It is well known that ergodicity and the strong law of large numbers (SLLN) play important
roles in stochastic control and stochastic approximations. For a class of regime-switching …

Probabilistic limit behaviors of numerical discretizations for time-homogeneous Markov processes

C Chen, T Dang, J Hong, G Song - arXiv preprint arXiv:2310.08227, 2023 - arxiv.org
In order to give quantitative estimates for approximating the ergodic limit, we investigate
probabilistic limit behaviors of time-averaging estimators of numerical discretizations for a …

The central limit theorems for integrable Hamiltonian systems perturbed by white noise

C Wang, Y Li - Journal of Differential Equations, 2025 - Elsevier
In this paper, we consider the dynamics of integrable stochastic Hamiltonian systems.
Utilizing the Nagaev-Guivarc'h method, we obtain several generalized results of the central …