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 …

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 …

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 …

We consider the incompressible 2D Navier-Stokes equations with periodic boundary
conditions driven by a deterministic time periodic forcing and a degenerate stochastic …

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 …

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 …

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 …

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 …

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 …

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 …