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Difference methods for stochastic partial differential equations. (English) Zbl 1010.60057
The deterministic theory of finite difference schemes is an important subject in order to approximate the solutions of partial differential equations. This article presents difference methods in order to approximate the solutions of stochastic partial differential equations of Itô-type, in particular hyperbolic equations. The main notions of deterministic difference methods, i.e. convergence, consistency, and stability, are developed for the stochastic case. It is shown that the proposed stochastic difference schemes for several partial differential equations have these properties.

MSC:
60H15 Stochastic partial differential equations (aspects of stochastic analysis)
65M06 Finite difference methods for initial value and initial-boundary value problems involving PDEs
65M12 Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs
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