Stochastic Differential Equations and Markov Diffusion Processes

Abstract

In this chapter we review a part of the theory of continuous parameter stochastic processes which is of interest for the study of Markov models of systems which arise in applications. With one exception the present chapter involves no ideas from control theory, and may be read independently of the rest of the book. (The exception is Theorem 9.2 about the Kalman-Bucy filter; the proof we give depends on the solution to the linear regulator problem.) In the chapter we emphasize material needed to discuss in a mathematically correct way optimal control of diffusion processes in Chap. VI.