Markov chain

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Markov chain

[′mar‚kȯf ‚chān]
(mathematics)
A Markov process whose state space is finite or countably infinite.

Markov Chain

 

a concept in probability theory that emerged from the works of the Russian mathematician A. A. Markov (the elder) that dealt with the study of sequences of dependent trials and sums of random variables associated with them. The development of the theory of Markov chains facilitated the creation of the general theory of Markov processes.

Markov chain

(probability)
(Named after Andrei Markov) A model of sequences of events where the probability of an event occurring depends upon the fact that a preceding event occurred.

A Markov process is governed by a Markov chain.

In simulation, the principle of the Markov chain is applied to the selection of samples from a probability density function to be applied to the model. Simscript II.5 uses this approach for some modelling functions.

References in periodicals archive ?
If we had known that 2008 was an unusually dry year before we used it to construct our Markov analysis, we would have known (or at least suspected) that its state transition matrix would not be representative for the ten-year period, and we would not have wasted our time using it for that purpose.
Specifically, we wanted to know if the Markov analysis method could detect measurable and generalizable differences between effective and ineffective students' use of basic counseling skills by examining the processes associated with their respective counseling sessions.
Although our primary interest was to see if the Markov analysis revealed measurable differences between students' sequences of skills when sorted by the raters' judgment of effectiveness, other measures of effectiveness might provide even clearer differences between the groups.
Wampold (1986) previously argued that the Markov analysis approach is only one of several sequential analyses that can be used.
It can be argued that the mathematical sophistication of Markov analysis is precisely that:
Markov analysis is highly mathematical in nature, being a derivative of probability theory.
Markov analysis attempts to describe a system as a series of stocks and flows (states and transitions).