Introduction to the Theory of Controlled Diffusion Processes

Abstract

The objective of Chapter 1 is to make the reader familiar with the general concepts, methods, and problems of the theory of controlled random diffusion processes. In Sections 1 and 2 we formulate the basic problems and indicate methods of solution. We omit rigorous proofs, our arguments being of a purely heuristic nature. In our opinion, the simplicity of the ideas at the basic level justifies our confidence in our ability to solve seemingly complex control problems. Many of the assertions in Sections 1 and 2 are proved rigorously further on in the book under appropriate conditions. In Section 3 we first explain heuristically how the notions of Section 2 can be applied in order to obtain estimates of various kinds, later making rigorous calculations for a specific example.