A splitting/polynomial chaos expansion approach for stochastic evolution equations

Abstract

In this paper, we combine deterministic splitting methods with a polynomial chaos expansion method for solving stochastic parabolic evolution problems. The stochastic differential equation is reduced to a system of deterministic equations that we solve explicitly by splitting methods. The method can be applied to a wide class of problems where the related stochastic processes are given uniquely in terms of stochastic polynomials. A comprehensive convergence analysis is provided and numerical experiments validate our approach.

28 pages, 3 figures, 1 table

References in corpus (2)

• Wiener chaos solutions of linear stochastic evolution equations
• The asymptotic error of chaos expansion approximations for stochastic differential equations