39 citations · 503 across the 77 of their papers we have counts for
6 papers · 2 filters
Discontinuous Stochastic Differential Equations Driven by Lévy Processes
Xicheng Zhang
In this article we prove the pathwise uniqueness for stochastic differential equations in $\mR^d$ with time-dependent Sobolev drifts, and driven by symmetric -stable processes p…
Stochastic Homeomorphism Flows of SDEs with Singular Drifts and Sobolev Diffusion Coefficients
Xicheng Zhang
In this paper we prove the stochastic homeomorphism flow property and the strong Feller property for stochastic differential equations with sigular time dependent drifts and Sobole…
Degenerate Irregular SDEs with Jumps and Application to Integro-Differential Equations of Fokker-Planck type
Xicheng Zhang
We investigate stochastic differential equations with jumps and irregular coefficients, and obtain the existence and uniqueness of generalized stochastic flows. Moreover, we also p…
Quasi Invariant Stochastic Flows of SDEs with Non-smooth Drifts on Riemannian Manifolds
Xicheng Zhang
In this article we prove that stochastic differential equation (SDE) with Sobolev drift on compact Riemannian manifold admits a unique -almost everywhere stochastic invertible f…
Stochastic Monge-Kantorovich Problem and its Duality
Xicheng Zhang
In this article we prove the existence of a stochastic optimal transference plan for a stochastic Monge-Kantorovich problem by measurable selection theorem. A stochastic version of…
Well-posedness and large deviation for degenerate SDEs with Sobolev coefficients
Xicheng Zhang
In this article we prove the existence and uniqueness for degenerate stochastic differential equations with Sobolev (possibly singular) drift and diffusion coefficients in a genera…