Implicit scheme for stochastic parabolic partial differential equations driven by space-time white noise. (English) Zbl 0893.60033

Gyöngy, István; Nualart, David

Potential Anal. 7, No. 4, 725-757 (1997).

The paper considers the numerical approximation of stochastic parabolic partial differential equations driven by space time white noise. The authors use an implicit approximation scheme similar to the Rothe method. They show almost sure convergence when the nonlinear terms are Lipschitz continuous functions. Using Malliavin calculus, they prove convergence in probability when the drifts are only measurable.

Reviewer: E.Platen (Canberra)

MSC:

60H10

Stochastic ordinary differential equations (aspects of stochastic analysis)

Keywords:

stochastic partial differential equation; numerical methods; Malliavin calculus