Xicheng Zhang

TL;DR: In this article, the authors studied the fractional smoothness of local times of general processes starting from the occupation time formula, and obtained the quasi-sure existence of the local times in the sense of the Malliavin calculus.

TL;DR: In this paper, the authors established the optimal regularity estimates for the Cauchy problem of stochastic kinetic equations with random coefficients in anisotropic Besov spaces, and obtained the existence and regularity of conditional probability densities under few assumptions.

TL;DR: In this paper, the set of functionals on abstract Wiener space in terms of the compact embedding theorems in finite dimensional Sobolev spaces was studied and several relatively compact families of random fields for the solutions to SDEs (and SPDEs) with coefficients satisfying some bounded assumptions, some stochastic integrals, and local times of diffusion processes.

TL;DR: In this article, a sufficient and necessary condition for a set in an abstract Wiener space (X, H, µ) to be relatively compact in L2(X, µ).

TL;DR: In this article, the authors proved the existence of local smooth solutions in Sobolev spaces for a class of second order quasi-linear parabolic partial differential equations (possibly degenerate) with smooth coefficients.