Finite Markov Chains and Markov Decision Processes

Abstract

Markov chains are important tools used for stochastic modeling in various areas of mathematical sciences. The first section of this article presents a survey of the basic notions of discrete-time Markov chains on finite state spaces together with several illustrative examples. Markov decision processes (MDPs), which are also known as stochastic dynamic programming or discrete-time stochastic control, are useful for decision making under uncertainty. The second section will provide a simple formulation of MDPs with finite state spaces and actions, and give two important algorithms for solving MDPs, value iteration and policy iteration, with an example on iPod shuffle.