Huang, Yan2015-10-132015-10-132015-08https://hdl.handle.net/11299/174784University of Minnesota M.S. thesis. August 2015. Major: Mathematics. Advisor: John Baxter. 1 computer file (PDF); iv, 35 pages.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.enErgodic TheoremMarkov ChainsStrong LawThesis or Dissertation