Markov Operators on a Banach Lattice and Their Applications

Abstract

Any Markov process is defined by a stochastic kernel. By using a stochastic kernel, we can define a Markov operator on a Banach lattice. Conversely, by using a Markov operator, we can define a Markov process. There is a close relationship between a Markov process and a Markov operator. In this chapter, we show the relation between a Markov process and a Markov operator. We show some applications of Markov operators concerned with dynamical systems and we mention the Jacobs-de Leeuw-Glicksberg decomposition which is induced by a Markov operator.