Difference Methods for Stochastic Partial Differential Equations

The present article focuses on the use of difference methods in order to approximate the solutions of stochastic partial differential equations of Ito-type, in particular hyperbolic equations. The main notions of deterministic difference methods, i.e. convergence, consistency, and stability, are developped for the stochastic case. It is shown that the proposed stochastic difference schemes for several partial differential equations have these properties.