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On the discretization in time of parabolic stochastic partial differential equations

Published online by Cambridge University Press:  15 April 2002

Jacques Printems
Jacques Printems*
Affiliation:
Centre de Mathématiques de l'Université de Paris 12, EA 2343, Université de Paris 12, 61 avenue du Général de Gaulle, 94010 Créteil Cedex, France. (printems@univ-paris12.fr)
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Abstract

We first generalize, in an abstract framework, results on the order of convergence of a semi-discretization in time by an implicit Euler scheme of a stochastic parabolic equation. In this part, all the coefficients are globally Lipchitz. The case when the nonlinearity is only locally Lipchitz is then treated. For the sake of simplicity, we restrict our attention to the Burgers equation. We are not able in this case to compute a pathwise order of the approximation, we introduce the weaker notion of order in probability and generalize in that context the results of the globally Lipschitz case.

Keywords

Stochastic partial differential equationssemi-discretized scheme for stochastic partial differential equationsEuler scheme.
Type
Research Article
Information
ESAIM: Mathematical Modelling and Numerical Analysis , Volume 35 , Issue 6 , November 2001 , pp. 1055 - 1078
Copyright
© EDP Sciences, SMAI, 2001

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