| The purpose of this paper is to explain the pointwise Ergodic Theorem and then to apply it to stationary Markov Chains. The Ergodic Theorem is a theorem which shows that the time-averages of a stationary sequence of random variables converge almost surely, and also gives a way to evaluate the limit of these averages. In the setting of Markov chains, the Ergodic Theorem can be used to obtain an important convergence fact about Markov chains. |
