Printems, Jacques
On the discretization in time of parabolic stochastic partial differential equations
ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique, Tome 35 (2001) no. 6 , p. 1055-1078
Zbl 0991.60051 | MR 1873517 | 1 citation dans Numdam
URL stable : http://www.numdam.org/item?id=M2AN_2001__35_6_1055_0

Classification:  60H15,  60F25,  60F99,  65C20,  60H35
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.

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