In this paper, we consider the averaging principle for one dimensional stochastic Burgers
equation with slow and fast time-scales. Under some suitable conditions, we show that the …

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 fast/slow systems driven by a fractional Brownian motion B with Hurst parameter
H∈(1 3, 1]. Surprisingly, the slow dynamic converges on suitable timescales to a limiting …

In this paper, we study the asymptotic behavior of a semi-linear slow-fast stochastic partial
differential equation with singular coefficients. Using the Poisson equation in Hilbert space …

We study random “perturbation” to the geodesic equation. The geodesic equation is
identified with a canonical differential equation on the orthonormal frame bundle driven by a …

In this paper, we study the diffusion approximation for singularly perturbed stochastic
reaction-diffusion equation with a fast oscillating term. The asymptotic limit for the original …

This work focuses on topics related to Hamiltonian stochastic differential equations with Lévy
noise. We first show that the phase flow of the stochastic system preserves symplectic …

In this paper, we establish a quantified asymptotic analysis for a semi-linear slow-fast
stochastic partial differential equation with Hölder coefficients. By studying the Poisson …

Motivated by collapsing of Riemannian manifolds and inhomogeneous scaling of left
invariant Riemannian metrics on a real Lie group G with a sub-group H, we introduce a …