39 citations · 503 across the 77 of their papers we have counts for
5 papers · 2 filters
Stochastic Volterra Equations in Banach Spaces and Stochastic Partial Differential Equations
Xicheng Zhang
In this paper, we first study the existence-uniqueness and large deviation estimate of solutions for stochastic Volterra integral equations with singular kernels in 2-smooth Banach…
A Stochastic Representation for Backward Incompressible Navier-Stokes Equations
Xicheng Zhang
By reversing the time variable we derive a stochastic representation for backward incompressible Navier-Stokes equations in terms of stochastic Lagrangian paths, which is similar t…
Stochastic Tamed 3D Navier-Stokes Equations: Existence, Uniqueness and Ergodicity
Michael Röckner, Xicheng Zhang
In this paper, we prove the existence of a unique strong solution to a stochastic tamed 3D Navier-Stokes equation in the whole space as well as in the periodic boundary case. Then,…
Smooth Solutions of Non-linear Stochastic Partial Differential Equations
Xicheng Zhang
In this paper, we study the regularities of solutions of nonlinear stochastic partial differential equations in the framework of Hilbert scales. Then we apply our general result to…
Freidlin-Wentzell's Large Deviations for Stochastic Evolution Equations
Jiagang Ren, Xicheng Zhang
We prove a Freidlin-Wentzell large deviation principle for general stochastic evolution equations with small perturbation multiplicative noises. In particular, our general result c…