A simulation of integral and derivative of the solution of a stochastici integral equation

Abstract

A stochastic integral equation corresponding to a probability space (Ω, Σω, Pω) is considered. This equation plays the role of a dynamical system in many problems of stochastic control with the control variable u(•) : R 1 → R m. One constructs stochastic processes η (1) (t), η (2) (t) connected with a Markov chain and with the space (Ω, Σω, Pω). The expected values of η (i) (t) (i = 1, 2) are respectively the expected value of an integral representation of a solution x(t) of the equation and that of its derivative x u (t).