Stationary Distributions of a Markov Chain

What is in this chapter? Let X _n be the state of a Markov chain at time n. Assume that X₀, the initial state of the chain, is distributed according to a distribution π. That is, assume that the probability that X₀ is in state i is π(i). Can we find a distribution π such that if X₀ has distribution π then X _n , for all times n, also has distribution π? Such a distribution is said to be stationary for the chain. This chapter deals with the existence of and the convergence to stationary distributions.