48 citations · 128 across the 30 of their papers we have counts for
26 papers · 1 filter
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…
Infinite-horizon time-inhomogeneous Kolmogorov equation and non-autonomous multi-scale stochastic systems
Ling Wang, Pengcheng Xia, Longjie Xie +1
We propose a unified approach, based on the infinite-horizon time-inhomogeneous Kolmogorov equation with a parameter, to study the asymptotic behavior of non-autonomous multi-scale…
Functional law of large numbers and central limit theorem for slow-fast McKean-Vlasov equations
Yun Li, Longjie Xie
In this paper, we study the asymptotic behavior of a fully-coupled slow-fast McKean-Vlasov stochastic system. Using the non-linear Poisson equation on Wasserstein space, we first e…
Poisson equation on Wasserstein space and diffusion approximations for McKean-Vlasov equation
Yun Li, Fuke Wu, Longjie Xie
We consider the fully-coupled McKean-Vlasov equation with multi-time-scale potentials, and all the coefficients depend on the distributions of both the slow component and the fast…