39 citations · 503 across the 77 of their papers we have counts for
5 papers · 2 filters
Hölder estimates for nonlocal-diffusion equations with drifts
Zhen-Qing Chen, Xicheng Zhang
We study a class of nonlocal-diffusion equations with drifts, and derive a priori -Hölder estimate for the solutions by using a purely probabilistic argument, where is an in…
Sobolev differentiable flows of SDEs with local Sobolev and super-linear growth coefficients
Longjie Xie, Xicheng Zhang
By establishing a characterization for Sobolev differentiability of random fields, we prove the weak differentiability of solutions to stochastic differential equations with local…
Stochastic differential equations with Sobolev diffusion and singular drift
Xicheng Zhang
In this paper we study properties of solutions to stochastic differential equations with Sobolev diffusion coefficients and singular drifts. The properties we study include stabili…
Fundamental solutions of nonlocal Hörmander's operators
Xicheng Zhang
Consider the following nonlocal integro-differential operator: for , $$ \cL^{(α)}_{σ,b} f(x):=\mbox{p.v.} \int_{|z|<δ}\frac{f(x+σ(x)z)-f(x)}{|z|^{d+α}}\dif z+b(x)\cdot\n…
Regularity of density for SDEs driven by degenerate Lévy noises
Yulin Song, Xicheng Zhang
By using Bismut's approach about the Malliavin calculus with jumps, we study the regularity of the distributional density for SDEs driven by degenerate additive Lévy noises. Under…