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.
Mots clés : stochastic partial differential equations, semi-discretized scheme for stochastic partial differential equations, Euler scheme
@article{M2AN_2001__35_6_1055_0,
author = {Printems, Jacques},
title = {On the discretization in time of parabolic stochastic partial differential equations},
journal = {ESAIM: Mod\'elisation math\'ematique et analyse num\'erique},
pages = {1055--1078},
publisher = {EDP-Sciences},
volume = {35},
number = {6},
year = {2001},
mrnumber = {1873517},
zbl = {0991.60051},
language = {en},
url = {http://www.numdam.org/item/M2AN_2001__35_6_1055_0/}
}
TY - JOUR AU - Printems, Jacques TI - On the discretization in time of parabolic stochastic partial differential equations JO - ESAIM: Modélisation mathématique et analyse numérique PY - 2001 SP - 1055 EP - 1078 VL - 35 IS - 6 PB - EDP-Sciences UR - http://www.numdam.org/item/M2AN_2001__35_6_1055_0/ LA - en ID - M2AN_2001__35_6_1055_0 ER -
%0 Journal Article %A Printems, Jacques %T On the discretization in time of parabolic stochastic partial differential equations %J ESAIM: Modélisation mathématique et analyse numérique %D 2001 %P 1055-1078 %V 35 %N 6 %I EDP-Sciences %U http://www.numdam.org/item/M2AN_2001__35_6_1055_0/ %G en %F M2AN_2001__35_6_1055_0
Printems, Jacques. On the discretization in time of parabolic stochastic partial differential equations. ESAIM: Modélisation mathématique et analyse numérique, Tome 35 (2001) no. 6, pp. 1055-1078. http://www.numdam.org/item/M2AN_2001__35_6_1055_0/
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