We establish a large deviation principle for the solutions of a class of stochastic partial differential equations with non-Lipschitz continuous coefficients. As an application, the large deviation principle is derived for super-Brownian motion and Fleming–Viot process.

We establish large deviation estimates for the optimal filter where the observation process is corrupted by a fractional Brownian motion. The observation process is transformed to an equivalent model which is driven by a standard Brownian motion. The large deviations in turn are established by...

The (Ξ,A)-Fleming–Viot process with mutation is a probability-measure-valued process whose moment dual is similar to that of the classical Fleming–Viot process except that Kingman’s coalescent is replaced by the Ξ-coalescent, the coalescent with simultaneous multiple collisions. We first...

An infinite system of stochastic differential equations for the locations and weights of a collection of particles is considered. The particles interact through their weighted empirical measure, V, and V is shown to be the unique solution of a nonlinear stochastic partial differential equation...

We study the long time limiting behavior of the occupation time of the superprocess over a stochastic flow introduced by Skoulakis and Adler (2001) [13]. The ergodic theorems for dimensions d=2 and d=3 are established. The proofs depend heavily on a characterization of the conditional...

In general, gradient estimates are very important and necessary for deriving convergence results in different geometric flows, and most of them are obtained by analytic methods. In this paper, we will apply a stochastic approach to systematically give gradient estimates for some important...

The paper is a continuation of our paper, Wang and Wang (2013) [13], Chen and Wang  [4], and it studies functional inequalities for non-local Dirichlet forms with finite range jumps or large jumps. Let α∈(0,2) and μV(dx)=CVe−V(x)dx be a probability measure. We present explicit and sharp...