48 citations · 128 across the 30 of their papers we have counts for
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Superposition principle for non-local Fokker-Planck operators
Michael Rockner, Longjie Xie, Xicheng Zhang
We prove the superposition principle for probability measure-valued solutions to non-local Fokker-Planck equations, which in turn yields the equivalence between martingale problems…
Averaging principle for slow-fast stochastic partial differential equations with Hölder continuous coefficients
Xiaobin Sun, Longjie Xie, Yingchao Xie
By using the technique of the Zvonkin's transformation and the classical Khasminkii's time discretization method, we prove the averaging principle for slow-fast stochastic partial…
-theory of stochastic differential equations
Pengcheng Xia, Longjie Xie, Xicheng Zhang +1
In this paper we show the weak differentiability of the unique strong solution with respect to the starting point as well as Bismut-Elworthy-Li's derivative formula for the fol…
Strong and weak convergence in the averaging principle for SDEs with Hölder coefficients
Michael Röckner, Xiaobin Sun, Longjie Xie
Using Zvonkin's transform and the Poisson equation in with a parameter, we prove the averaging principle for stochastic differential equations with time-dependent Hölder cont…
Blowup solutions of Grushin's operator
Guangying Lv, Jinlong Wei, Longjie Xie
In this note, we consider the blowup phenomenon of Grushin's operator. By using the knowledge of probability, we first get expression of heat kernel of Grushin's operator. Then by…