# 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 ?
the probability that the Markov chain moves from state i to state j, in h steps and the matrix
We have compared the analytical results of the proposed model by taking into account case1 (considering the special state (i,-1)) and case2 (without considering the special state (i,-1)) of the Markov chain model.
All states of the underlying digraph of the Markov chain are assumed to be accessible from the initial state.
The application developed from the mathematical model based on the Markov chain theory allows for the reduction of the distance travelled by the transfer-transport system and of its functioning time at the moment of loading and unloading of parts.
The most critical step in using Markov chain is to determine the transition probability matrix P.
The state probability equations for this Markov chain are
Droughts occurred in the city of synoptic stations shoushtar by PNPI and SPI indices was performed and the results are listed in Table 3 Comparison Between them, the proximity of the two parameters was observed As was observed in the Markov chain using PNPI index more than 81% probability gives a normal water year.
The development of TPM is one essential component in using Markov Chain based models.
In this study, a Markov chain is used to model the hitting of major league baseball players over the course of a season.
One of the advantages of using Markov chain model is that it allows computing steady state probabilities of all system states, which helps to estimate probabilities of rare events and failure scenarios.

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