HAL: hal-00669470, version 1

arXiv: 1202.2706

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Analysis of a HMM time-discretization scheme for a system of Stochastic PDE's

Charles-Edouard Bréhier 1

(2012-02-13)

We consider the discretization in time of a system of parabolic stochastic partial differential equations with slow and fast components; the fast equation is driven by an additive space-time white noise. The numerical method is inspired by the Averaging Principle satisfied by this system, and fits to the framework of Heterogeneous Multiscale Methods.The slow and the fast components are approximated with two coupled numerical semi-implicit Euler schemes depending on two different timestep sizes. We derive bounds of the approximation error on the slow component in the strong sense - approximation of trajectories - and in the weak sense - approximation of the laws. The estimates generalize the results of \cite{E-L-V} in the case of infinite dimensional processes.

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 – Heterogeneous Multiscale Method – Time Scale Separation – Euler Scheme – Strong and Weak Approximation

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From: Maryse Collin <>

Submitted on: Monday, 13 February 2012 12:00:33

Updated on: Monday, 13 February 2012 13:29:48