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Markov Sequence


A sequence X_1, X_2, ... of random variates is called Markov (or Markoff) if, for any n,

 F(X_n|X_(n-1),X_(n-2),...,X_1)=F(X_n|X_(n-1)),

i.e., if the conditional distribution F of X_n assuming X_(n-1), X_(n-2), ..., X_1 equals the conditional distribution F of X_n assuming only X_(n-1) (Papoulis 1984, pp. 528-529). The transitional densities of a Markov sequence satisfy the Chapman-Kolmogorov equation.


See also

Chapman-Kolmogorov Equation, Markov Chain

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References

Papoulis, A. "Markoff Sequences." §15-3 in Probability, Random Variables, and Stochastic Processes, 2nd ed. New York: McGraw-Hill, pp. 528-535, 1984.

Referenced on Wolfram|Alpha

Markov Sequence

Cite this as:

Weisstein, Eric W. "Markov Sequence." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/MarkovSequence.html

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