Stationary Stochastic Viscosity Solutions of SPDEs

Abstract

In this paper we aim to find the stationary stochastic viscosity solutions of a parabolic type SPDEs through the infinite horizon backward doubly stochastic differential equations (BDSDEs). For this, we study the existence, uniqueness and regularity of solutions of the corresponding infinite horizon BDSDEs as well as the "perfection procedure" applied to the solutions of BDSDEs. At last the "perfect" stationary stochastic viscosity solutions of SPDEs constructed by solutions of corresponding BDSDEs are obtained.