The topic of Markov chains is a well-developed topic in probability. There are many fine expositions of Markov chains (e.g., Bremaud, 2008; Feller, 1968; Hoel, Port, & Stone, 1972; Kemeny & Snell, 1960). Those expositions and others have informed this concise entry on Markov chains, which is not intended to exhaust the topic of Markov chains. The topic is just too capacious for that. This entry provides an exposition of a judicious sampling of the major ideas, concepts, and methods regarding the topic.
Andrei Andreevich Markov (1856–1922) formulated the seminal concept in the field of probability later known as the Markov chain. Markov was an eminent Russian mathematician who served as a professor in the Academy of Sciences at the University of St. Petersburg. ...
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