1490 articles – 5641 references  [version française]
 HAL: hal-00669462, version 1
 arXiv: 1202.2707
 Approximation of the invariant measure with an Euler scheme for Stochastic PDE's driven by Space-Time White Noise
 (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 AnalysisMathematics/Probability
 Keyword(s): Stochastic Partial Differential Equations – Invariant measures and Ergodicity – Weak Approximation – Euler scheme
Attached file list to this document:
 PDF
 Invar_num.pdf(304.7 KB)
 PS
 Invar_num.ps(1 MB)
 hal-00669462, version 1 http://hal.archives-ouvertes.fr/hal-00669462 oai:hal.archives-ouvertes.fr:hal-00669462 From: Maryse Collin <> Submitted on: Monday, 13 February 2012 11:56:15 Updated on: Monday, 13 February 2012 13:30:47