4 papers
Uniform-in-time diffusion approximations for multiscale stochastic systems
Longjie Xie, Xicheng Zhang
This paper establishes a quantitative, uniform-in-time diffusion approximation for the joint law of a broad class of fully coupled multiscale stochastic systems. We derive a precis…
Derivative estimates for SDEs with singular and unbounded coefficients
Pengcheng Xia, Longjie Xie, Xicheng Zhang
We develop a unified PDE-probabilistic framework for pointwise gradient and Hessian estimates of Markov semigroups associated with stochastic differential equations with singular a…
Asymptotic limit of fully coupled multi-scale non-linear stochastic system: the non-autonomous approximation method
Yuewen Hou, Yun Li, Longjie Xie
In this paper, we develop a novel argument, the non-autonomous approximation method, to seek the asymptotic limits of the fully coupled multi-scale McKean-Vlasov stochastic systems…
Time inhomogeneous Poisson equations and non-autonomous multi-scale stochastic systems
Ling Wang, Pengcheng Xia, Longjie Xie +1
We develop a new tool, the time inhomogeneous Poisson equation in the whole space and with a terminal condition at infinity, to study the asymptotic behavior of the non-autonomous…