Basics of Applied Stochastic Processes

Part of the series Probability and Its Applications pp 1-98

Markov Chains

  • Richard SerfozoAffiliated withGeorgia Institute of Technology, School of Industrial & Systems Engineering Email author 

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A sequence of random variables \( X_0,X_1,... \) with values in a countable set S is a Markov chain if at any time n, the future states (or values) \( X_{n+1}, X_{n+2},... \) depend on the history \( X_0,...,X_n \) only through the present state \( X_n \).