No abstract

Using analytical methods, we prove existence uniqueness and estimates for s.p.d.e. of the type

No abstract

In this paper we prove L p estimates (p 2) for the uniform norm of the paths of solutions of quasilinear stochastic partial differential equations (SPDE) of parabolic type. Our method is based on a version of Moser's iteration scheme developed by Aronson and Serrin in the context of non-linear parabolic PDE.

We prove an existence and uniqueness result for the obstacle problem of quasilinear parabolic stochastic PDEs. The method is based on the probabilistic interpretation of the solution by using the backward doubly stochastic differential equation.