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DISCRETIZATION OF STATIONARY SOLUTIONS OF SPDE'S BY EXTERNAL APPROXIMATION IN SPACE AND TIME

A. OGROWSKY

Institut für Mathematik, Fakultät EIM, Universität Paderborn, Warburger Straße 100, 33098 Paderborn, Germany

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and

B. SCHMALFUSS

Institut für Mathematik, Fakultät EIM, Universität Paderborn, Warburger Straße 100, 33098 Paderborn, Germany

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https://doi.org/10.1142/S0218127410027398Cited by:1 (Source: Crossref)

Abstract

We consider a stochastic partial differential equation with additive noise satisfying a strong dissipativity condition for the nonlinear term such that this equation has a random fixed point. The goal of this article is to approximate this fixed point by space and space-time discretizations of a stochastic differential equation or more precisely, a conjugate random partial differential equation. For these discretizations external schemes are used. We show the convergence of the random fixed points of the space and space-time discretizations to the random fixed point of the original partial differential equation.

Dedicated to the memory of Valery S. Melnik

Keywords:

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