HAL: hal-00669462, version 1

arXiv: 1202.2707

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Approximation of the invariant measure with an Euler scheme for Stochastic PDE's driven by Space-Time White Noise

Charles-Edouard Bréhier 1

(2012-02-13)

In this article, we consider a stochastic PDE of parabolic type, driven by a space-time white-noise, and its numerical discretization in time with a semi-implicit Euler scheme. When the nonlinearity is assumed to be bounded, then a dissipativity assumption is satisfied, which ensures that the SDPE admits a unique invariant probability measure, which is ergodic and strongly mixing - with exponential convergence to equilibrium. Considering test functions of class $\mathcal{C}^2$, bounded and with bounded derivatives, we prove that we can approximate this invariant measure using the numerical scheme, with order $1/2$ with respect to the time step.

1:	Institut de Recherche Mathématique de Rennes (IRMAR)
	CNRS : UMR6625 – Université de Rennes 1 – École normale supérieure de Cachan - ENS Cachan – Institut National des Sciences Appliquées (INSA) : - RENNES – Université de Rennes II - Haute Bretagne

Research team: Analyse numérique, Processus stochastiques

Subject

:

Mathematics/Numerical Analysis Mathematics/Probability

Keyword(s): Stochastic Partial Differential Equations – Invariant measures and Ergodicity – Weak Approximation – Euler scheme

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From: Maryse Collin <>

Submitted on: Monday, 13 February 2012 11:56:15

Updated on: Monday, 13 February 2012 13:30:47