GENERAL THEOREMS FOR NUMERICAL APPROXIMATION OF STOCHASTIC PROCESSES ON THE HILBERT SPACEH2((0;T );; IR d )

General theorems for the numerical approximation on the separable Hilbert space H2((0; T ); ; IR d ) of cadlag, (Ft)-adapted stochastic processes with -integrable second moments is presented for nonrandom intervals (0; T ) and positive measure . The use of the theorems is illustrated by the special case of systems of ordinary stochastic differential equations (SDEs) and their numerical approximation given by the drift-implicit Euler method under one-sided Lipschitz-type conditions.