In this paper, we directly prove the existence and uniqueness of a strong solution of the stochastic differential equations with reflecting boundary under the assumption of non-degenerate diffusion coefficient and measurable drift. Moreover, a Wong-Zakai type approximation theorem is obtained...

Stochastic partial differential equations (SPDEs) of parabolic type driven by (pure) Poisson white noise are investigated in this paper. These equations are interpreted as stochastic integral equations of the jump type involving evolution kernels. Existence and uniqueness of the solution is...

We prove that for a given symmetric Dirichlet form of type g(u, v) = [integral operator]E<A(z)[backward difference]u(z), [backward difference]v(z)>h[mu](dz) with E = C0[0, 1] and H = classical Cameron-Martin space the corresponding diffusion process (under P[mu]) can be decomposed into a forward and a backward E-valued martingale. The construction of...</a(z)[backward>

In this paper, we establish a small time large deviation principle for diffusion processes on configuration spaces.

Due to technical reasons, existing results concerning Harnack type inequalities for SPDEs with multiplicative noise apply only to the case where the coefficient in the noise term is a Hilbert–Schmidt perturbation of a constant bounded operator. In this paper we obtained gradient estimates,...

In this article, we establish a large deviation principle for invariant measures of solutions of stochastic partial differential equations with two reflecting walls driven by a space–time white noise.

We study the dynamics of the Burgers equation on the unit interval driven by affine linear noise. Mild solutions of the Burgers stochastic partial differential equation generate a smooth perfect and locally compacting cocycle on the energy space. Using multiplicative ergodic theory techniques,...

In the first part of this paper, we prove the uniqueness of the solutions of SPDEs with reflection, which was left open in the paper [C. Donati-Martin, E. Pardoux, White noise driven SPDEs with reflection, Probab. Theory Related Fields 95 (1993) 1-24]. We also obtain the existence of the...

This article establishes existence and uniqueness of solutions to two classes of stochastic systems with finite memory subject to anticipating initial conditions which are sufficiently smooth in the Malliavin sense. The two classes are semilinear stochastic functional differential equations...

In this paper, we obtain a characterization of invariant measures of stochastic evolution equations and stochastic partial differential equations of pure jump type. As an application, it is shown that the equation has a unique invariant probability measure under some reasonable conditions.