39 citations · 503 across the 77 of their papers we have counts for
5 papers · 2 filters
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…
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'…