Geodesic
On the discretization in time of parabolic stochastic partial differential equations
ESAIM: Mathematical Modelling and Numerical Analysis , Tome 35 (2001) no. 6, pp. 1055-1078

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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.

Classification : 60H15, 60F25, 60F99, 65C20, 60H35
Keywords: stochastic partial differential equations, semi-discretized scheme for stochastic partial differential equations, Euler scheme 
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     author = {Printems, Jacques},
     title = {On the discretization in time of parabolic stochastic partial differential equations},
     journal = {ESAIM: Mathematical Modelling and Numerical Analysis },
     pages = {1055--1078},
     publisher = {EDP-Sciences},
     volume = {35},
     number = {6},
     year = {2001},
     mrnumber = {1873517},
     zbl = {0991.60051},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/M2AN_2001__35_6_1055_0/}
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Printems, Jacques. On the discretization in time of parabolic stochastic partial differential equations. ESAIM: Mathematical Modelling and Numerical Analysis , Tome 35 (2001) no. 6, pp. 1055-1078. http://geodesic.mathdoc.fr/item/M2AN_2001__35_6_1055_0/