A Markov chain is collection of random variables (where the index runs through 0, 1, ...) having the property that, given the
present, the future is conditionally independent of the past.
In other words,
If a Markov sequence of random variates take the discrete values , ..., , then
and the sequence
is called a Markov chain (Papoulis 1984, p. 532).
A simple random walk is an example of a Markov
chain.
The Season 1 episode "Man Hunt " (2005) of the television crime drama NUMB3RS
features Markov chains.
See also Conditional Probability ,
Independent Events ,
Markov
Sequence ,
Monte Carlo Method ,
Random
Walk
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References Gamerman, D. Markov Chain Monte Carlo: Stochastic Simulation for Bayesian Inference. Boca Raton,
FL: CRC Press, 1997. Gilks, W. R.; Richardson, S.; and Spiegelhalter,
D. J. (Eds.). Markov
Chain Monte Carlo in Practice. Boca Raton, FL: Chapman & Hall, 1996. Grimmett,
G. and Stirzaker, D. Probability
and Random Processes, 2nd ed. Oxford, England: Oxford University Press, 1992. Harary,
F. Graph
Theory. Reading, MA: Addison-Wesley, p. 6, 1994. Kallenberg,
O. Foundations
of Modern Probability. New York: Springer-Verlag, 1997. Kemeny,
J. G. and Snell, J. L. Finite
Markov Chains. New York: Springer-Verlag, 1976. Papoulis, A.
"Brownian Movement and Markoff Processes." Ch. 15 in Probability,
Random Variables, and Stochastic Processes, 2nd ed. New York: McGraw-Hill,
pp. 515-553, 1984. Stewart, W. J. Introduction
to the Numerical Solution of Markov Chains. Princeton, NJ: Princeton University
Press, 1995. Referenced on Wolfram|Alpha Markov Chain
Cite this as:
Weisstein, Eric W. "Markov Chain." From
MathWorld --A Wolfram Web Resource. https://mathworld.wolfram.com/MarkovChain.html
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