Let be a real-valued fractional Brownian sheet. Consider the (, ) Gaussian random field defined by , where are independent copies of . In this paper, the existence and joint continuity of the local times of are established

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 this paper, we establish the existence and uniqueness of solutions of systems of stochastic partial differential equations (SPDEs) with reflection in a convex domain. The lack of comparison theorems for systems of SPDEs makes things delicate.

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...