ON THE SIMULATION OF STOCHASTIC PROCESSES WITH CONTINUOUS STATE AND PARAMETER SPACE.

This paper deals with the hybrid and digital simulation of some important classes of stochastic processes: diffusion processes and differential equations with random parameters and/or random right hand side. Under certain assumptions these processes may be modeled by the solutions of stochastic differential equations of the Ito type. Various methods of how to simulate these solutions on hybrid and digital computers are discussed. It is shown that the stochastic versions of some well-known deterministic methods have to be modified in order to obtain a correct simulation. Numerical results are justified by convergence theorems.