# On the discretization in time of parabolic stochastic partial differential equations

ESAIM: Mathematical Modelling and Numerical Analysis (2010)

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

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topPrintems, Jacques. "On the discretization in time of parabolic stochastic partial differential equations." ESAIM: Mathematical Modelling and Numerical Analysis 35.6 (2010): 1055-1078. <http://eudml.org/doc/197506>.

@article{Printems2010,

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},

keywords = {Stochastic partial differential equations; semi-discretized scheme for stochastic partial differential equations; Euler scheme.; stochastic partial differential equation; semi-discretization; Euler scheme},

language = {eng},

month = {3},

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/197506},

volume = {35},

year = {2010},

}

TY - JOUR

AU - Printems, Jacques

TI - On the discretization in time of parabolic stochastic partial differential equations

JO - ESAIM: Mathematical Modelling and Numerical Analysis

DA - 2010/3//

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; Euler scheme

UR - http://eudml.org/doc/197506

ER -

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