We consider a Poisson equation in R d for the elliptic operator corresponding to an ergodic
diffusion process. Optimal regularity and smoothness with respect to the parameter are …

We study the asymptotic behavior for an inhomogeneous multiscale stochastic dynamical
system with non-smooth coefficients. Depending on the averaging regime and the …

We study Poisson equations and averaging for Stochastic Differential Equations (SDEs).
Poisson equations are essential tools in both probability theory and partial differential …

In this paper, we consider a fully-coupled slow–fast system of McKean–Vlasov stochastic
differential equations with full dependence on the slow and fast component and on the law …

We consider a collection of fully coupled weakly interacting diffusion processes moving in a
two-scale environment. We study the moderate deviations principle of the empirical …

We consider a collection of weakly interacting diffusion processes moving in a two-scale
locally periodic environment. We study the large deviations principle of the empirical …

In this paper, we prove the moderate deviations principle (MDP) for a general system of slow-
fast dynamics. We provide a unified approach, based on weak convergence ideas and …

In this paper, we first establish general bounds on the Fisher information distance to the
class of normal distributions of Malliavin differentiable random variables. We then study the …

We investigate three types of averaging principles and the normal deviation for multi-scale
stochastic differential equations (in short, SDEs) with polynomial nonlinearity. More …

This work concerns about multiscale multivalued McKean-Vlasov stochastic systems. First of
all, we establish the well-posedness for multivalued McKean-Vlasov stochastic systems …