Siberian Mathematical Journal

, Volume 31, Issue 1, pp 159–162 | Cite as

Invariance principle for the sum of random variables defined on a homogeneous Markov chain

  • N. V. Gizbrekht
Article
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Keywords

Markov Chain Invariance Principle Homogeneous Markov Chain 

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Literature Cited

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    P. Billingsley, “The invariance principle for dependent random variables,” Trans. Am Math. Soc.,83, No. 1, 250–268 (1956).Google Scholar
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    Sh. K. Formanov, “Invariance principles for homogeneous Markov chains,” Dokl. Akad. Nauk SSSR,221, No. 1, 42–44 (1975).Google Scholar
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    P. P. Gudinas, “Invariance principle for nonhomogeneous Markov chains,” Lit. Mat. Sb.,XVII, No. 1, 63–73 (1977).Google Scholar
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    L. G. Gorostiza, “Convergence of transport processes with radially symmetric direction changes, and chain molecules,” J. Appl. Probab.,12, No. 4, 812–816 (1975).Google Scholar
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    S. G. Nagaev, and N. V. Ginzbrekht, “A scheme of a random walk describing the particles transport,” Trudy Inst. Mat. Akad. Nauk SSSR, Siberian Branch, in: Limit Theorems of Probability Theory [in Russian], Vol. 5 (1985), pp. 103–126.Google Scholar
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    P. Billingsley, Convergence of Probability Measures, Wiley, New York (1968).Google Scholar
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    I. I. Gikhman, and A. V. Skorokhod, Theory of Random Processes [in Russian], Nauka, Moscow (1971).Google Scholar

Copyright information

© Plenum Publishing Corporation 1990

Authors and Affiliations

  • N. V. Gizbrekht

There are no affiliations available

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