On the discretization in time of parabolic stochastic partial differential equations

Jacques Printems

ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique (2001)

  • Volume: 35, Issue: 6, page 1055-1078
  • ISSN: 0764-583X

Abstract

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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.

How to cite

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Printems, Jacques. "On the discretization in time of parabolic stochastic partial differential equations." ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique 35.6 (2001): 1055-1078. <http://eudml.org/doc/194086>.

@article{Printems2001,
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.},
author = {Printems, Jacques},
journal = {ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique},
keywords = {stochastic partial differential equations; semi-discretized scheme for stochastic partial differential equations; Euler scheme; stochastic partial differential equation; semi-discretization},
language = {eng},
number = {6},
pages = {1055-1078},
publisher = {EDP-Sciences},
title = {On the discretization in time of parabolic stochastic partial differential equations},
url = {http://eudml.org/doc/194086},
volume = {35},
year = {2001},
}

TY - JOUR
AU - Printems, Jacques
TI - On the discretization in time of parabolic stochastic partial differential equations
JO - ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique
PY - 2001
PB - EDP-Sciences
VL - 35
IS - 6
SP - 1055
EP - 1078
AB - 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.
LA - eng
KW - stochastic partial differential equations; semi-discretized scheme for stochastic partial differential equations; Euler scheme; stochastic partial differential equation; semi-discretization
UR - http://eudml.org/doc/194086
ER -

References

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