A Mini-Course on Stochastic Control

Abstract

This note is addressed to giving a short introduction to control theory of stochastic systems, governed by stochastic differential equations in both finite and infinite dimensions. We will mainly explain the new phenomenon and difficulties in the study of controllability and optimal control problems for these sort of equations. In particular, we will show by some examples that both the formulation of stochastic control problems and the tools to solve them may differ considerably from their deterministic counterpart.

This is a lecture notes of a short introduction to stochastic control. It was written for the LIASFMA (Sino-French International Associated Laboratory for Applied Mathematics) Autumn School "Control and Inverse Problems of Partial Differential Equations" at Zhejiang University, Hangzhou, China from October 17 to October 22, 2016