39 citations · 503 across the 77 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…
A discretized version of Krylov's estimate and its applications
Xicheng Zhang
In this paper we prove a discretized version of Krylov's estimate for discretized Itô's processes. As applications, we study the weak and strong convergences for Euler's approximat…
-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…
Stochastic Lagrangian path for Leray solutions of 3D Navier-Stokes equations
Xicheng Zhang, Guohuan Zhao
In this paper we show the existence of stochastic Lagrangian particle trajectory for Leray's solution of 3D Navier-Stokes equations. More precisely, for any Leray's solution ${\mat…
Schauder's estimate for nonlocal kinetic equations and its applications
Zimo Hao, Mingyan Wu, Xicheng Zhang
In this paper we develop a new method based on Littlewood-Paley's decomposition and heat kernel estimates of integral form, to establish Schauder's estimate for the following degen…
Hörmander's hypoelliptic theorem for nonlocal operators
Zimo Hao, Xuhui Peng, Xicheng Zhang
In this paper we show the Hörmander hypoelliptic theorem for nonlocal operators by a purely probabilistic method: the Malliavin calculus. Roughly speaking, under general Hörmander'…