Ranté Markov: Béda antarrépisi

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Dina [[matematik]], '''ranté Markov''' nyaéta [[prosés stokastik]] nu ngagunakeun [[Markov property]].
Salaku prosés, jarak ti heula taya hubunganana jeung jarak ayeuna di dipikanyaho.
 
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tapi Markov digunakeun oge di luar widang matematika, saperti [[law of large numbers|hukum wilangan gede]] dina kajadian anu pakait.
 
== Sifat ranté Markov ==
 
Ranté Markov dicirikeun ku conditional distribution
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Ieu ngarupakeun versi [[Frobenius-Perron equation]].
Didinya aya hiji atawa leuwih ''tetapan'' distribusi ππ saperti
 
:<math> \pi(X) = \int P(X|Y)\,\pi(Y)\,dY</math>
 
numana ''Y'' ngan sakadar ngaran variabel integrasi.
Saperti distribution &pi;π disebut ''stationary distribution'' atawa ''steady-state distribution''.
Stationary distribution nyaeta [[eigenfunction]] tina fungsi ''conditional distribution'', nu pakait jeung [[eigenvalue]] 1.
 
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= \int_A \pi(X)\,dX = \mu_{\pi}(A) </math>
 
where &mu;μ<sub>&pi;π</sub> is the measure induced by &pi;π.
This makes it possible to approximate the stationary distribution by a [[histogram]] or other density estimate of a sequence of samples.
 
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A matrix is a [[stochastic matrix]] if and only if it is the matrix of transition probabilities of some Markov chain.
 
== Scientific applications ==
 
Markov chains are used to model various processes in [[queueing theory]] and [[statistics]], and can also be used as a signal model in [[entropy coding]] techniques such as [[arithmetic coding]]. Markov chains also have many biological applications, particularly [[population process]]es, which are useful in modelling processes that are (at least) analogous to biological populations. Markov chains have been used in [[bioinformatics]] as well. An example is the [[genemark algorithm]] for coding region/gene prediction.
 
Markov processes can also be used to generate superficially "real-looking" text given a sample document: they are used in various pieces of recreational "parody generator" software (see [[Jeff Harrison]]).
 
== Tempo oge ==
 
* [[Hidden Markov model]]
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== Rujukan ==
 
* A.A. Markov. "Rasprostranenie zakona bol'shih chisel na velichiny, zavisyaschie drug ot druga". ''Izvestiya Fiziko-matematicheskogo obschestva pri Kazanskom universitete'', 2-ya seriya, tom 15, pp 135-156, 1906.
 
* A.A. Markov. "Extension of the limit theorems of probability theory to a sum of variables connected in a chain". reprinted in Appendix B of: R. Howard. ''Dynamic Probabilistic Systems, volume 1: Markov Chains''. John Wiley and Sons, 1971.
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* Leo Breiman. ''Probability''. Original edition published by Addison-Wesley, 1968; reprinted by Society for Industrial and Applied Mathematics, 1992. ISBN 0-89871-296-3. ''(See Chapter 7.)''
 
* J.L. Doob. ''Stochastic Processes''. New York: John Wiley and Sons, 1953. ISBN 0-471-52369-0.
 
== Tumbu kaluar ==
 
* [http://crypto.mat.sbg.ac.at/~ste/diss/node6.html Markov Chains]
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* [http://www.gnu.org/software/emacs/manual/html_node/emacs_473.html Disassociated Press] in [[Emacs]] approximates a Markov process
 
[[CategoryKategori:Téori probabilitas]]
[[CategoryKategori:Prosés stokastik]]
 
[[ar:سلسلة ماركوف]]
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[[el:Αλυσίδα Μαρκόφ]]
[[en:Markov chain]]
[[es:Cadena de MárkovMarkov]]
[[et:Markovi ahel]]
[[fa:فرایند مارکف]]