THE APPLICATION OF WHEP TECHNIQUE ON STOCHASTIC PARTIAL DIFFERENTIAL EQUATIONS

Abstract

The Wiener-Hermite expansion was applied successfully on some linear andnonlinear ordinary stochastic differential equations. The author introducedthe WHEP technique as an efficient algorithm to solve the perturbed ordinarystochastic differential equations. In this paper, the WHEP algorithm isapplied on a nonlinearly perturbed stochastic partial differential equations. The existence of the solution as a power series in the perturbationparameter is proved. Then, the Gaussian part of the solution is obtained infirst order approximation by the use of the WHEP technique.