Fractional step method for stochastic evolution equations

Abstract

This paper deals with the fractional step method in the analysis of stochastic partial differential equations (SPDEs) and their generalizations. Three types of problems are investigated. The first one is the study of invariant sets for the solution of the stochastic equations. The second one is existence of solutions for certain stochastic partial differential equations describing the mass distribution of a system of diffusing and reacting particles; the assumptions in the traditional approaches to SPDEs are not satisfied for this SPDE. The third type of problems is the numerical one: we construct solutions of a class of quasilinear stochastic differential equations of parabolic type using the fractional step method with the decomposition into linearized “drift” and pure “diffusion” equations.