Forschungsgruppe Angewandte Statistik
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2020-11-25 [ ]

New publication: A splitting/ polynomial chaos expansion approach for stochastic evolution equations

A splitting/ polynomial chaos expansion approach for stochastic evolution equations

A. Kofler, T. Levajkovic, H. Mena, A. Ostermann

Published: 4. November. 2020

In: Journal of Evolution Equation (2020)

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 efficiently 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.