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 ?
Frydman, Halina, Jarl Kallberg, and Duen-Li Kao (1985) Testing the Adequacy of Markov Chain and Mover-Stayer Models as Representations of Credit Behavior.
On the Limiting Behaviour of a Non-homogeneous Markov Chain Model in Manpower Systems.
Then, the probability that the loan is in state i at period t+l is expressed as a Markov chain, as follows:
In this paper we consider the family of Markov chains associated to the parametrized matrix
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.
The reasonable fitting of fatigue test data of carbon-fiber composite specimen is obtained using a simple Markov chain model with states of space based on random Daniels' sequence assuming the decrease of local tensile strength of LIs in comparison with tensile strength of single LI and some time scale factor.
The vertical change of textural layers is assumed to be a 1-D Markov chain that can be described by a TPM.
2 The descent set process of a deck of n distinct cards under a- shuffling is a Markov chain, whose transition matrix [[bar.
t+1] = j, we say that the Markov chain visits the states i and j at times t and t + 1, respectively, and that the Markov chain transitions from i to j at time t + 1.
Markov chain is a stochastic process that handles the uncertainty condition of road system performance through time.
A Markov chain defined on different payment states of a mortgage loan allows one to define and calculate a health index on the loan portfolio which can be used as a performance measure of that portfolio.