On the Solutions of a Stochastic Control System. II

Abstract

This paper presents generalizations of the work in [1], [2] to include controlled stochastic processes which take values in a certain class of Frechet spaces. The crucial result is an extension of Girsanov’s technique for defining solutions of stochastic differential equations by an absolutely continuous transformation of measures. The result is used to prove existence results for stochastic control problems and for a class of two-person zero sum games.