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Discretization of stationary solutions of SPDE’s by external approximation in space and time. (English) Zbl 1202.60102

Summary: 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.

MSC:

60H15 Stochastic partial differential equations (aspects of stochastic analysis)
37H10 Generation, random and stochastic difference and differential equations
65Mxx Numerical methods for partial differential equations, initial value and time-dependent initial-boundary value problems
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