39 citations · 503 across the 77 of their papers we have counts for
7 papers · 1 filter
Heat kernel estimates for critical fractional diffusion operator
Longjie Xie, Xicheng Zhang
In this work we construct the heat kernel of the 1/2-order Laplacian perturbed by the first-order gradient term in Hölder space and the zero-order potential term in generalized Kat…
Exponential Ergodicity of stochastic Burgers equations driven by -stable processes
Zhao Dong, Lihu Xu, Xicheng Zhang
In this work, we prove the strong Feller property and the exponential ergodicity of stochastic Burgers equations driven by -subordinated cylindrical Brownian motions with $α\i…
Densities for SDEs driven by degenerate -stable processes
Xicheng Zhang
In this work, by using the Malliavin calculus, under Hörmander's condition, we prove the existence of distributional densities for the solutions of stochastic differential equation…
-solvability of nonlocal parabolic equations with spatial dependent and non-smooth kernelsXiche
Xicheng Zhang
In this paper we prove the optimal -solvability of nonlocal parabolic equation with spatial dependent and non-smooth kernels.
Heat Kernel for Fractional Diffusion Operators with Perturbations
Feng-Yu Wang, Xicheng Zhang
Let be an elliptic differential operator on a complete connected Riemannian manifold such that the associated heat kernel has two-sided Gaussian bounds as well as a Gaussia…
Derivative formula and gradient estimate for SDEs driven by -stable processes
Xicheng Zhang
In this paper we prove a derivative formula of Bismut-Elworthy-Li's type as well as gradient estimate for stochastic differential equations driven by -stable noises, where $α\in…