Stochastic control and games under arbitrarily dependent noises

Abstract

In the paper the two forms of the separation principle for partially observable linear systems are discussed. It is shown that the classic form of the separation principle is valid while the past of the observations and the future of the state noise are independent. If the they are dependent then the separation principle changes its form that is called an extended separation principle. A detailed proof of the extended separation principle for control and game problems are given and its application to existence of saddle points is considered.