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Teoriya Veroyatnostei i ee Primeneniya, 1999, Volume 44, Issue 1, Pages 14–33
DOI: https://doi.org/10.4213/tvp595 (Mi tvp595) 		 
This article is cited in 6 scientific papers (total in 6 papers)

Cramér asymptotics in a system with slow and fast Markovian motions

V. I. Bakhtin

Belarusian State University, Faculty of Physics
Full-text PDF (2479 kB) Citations (6)
DOI: https://doi.org/10.4213/tvp595
Abstract: A cascade with fast and slow motions is considered in which the rapid motions constitute an ergodic Markov chain. Asymptotics of the probabilities of large deviations of the Cramér type are calculated for the difference between the slow component of the cascade trajectory and some averaged trajectory. The Taylor expansions in the powers of a small parameter are calculated for the semi-invariants of the difference which are smoothly dependent on time.
Keywords: averaging, system with fast and slow motions, Markov chain, semi-invariant, large deviations, Cramér's asymptotics.
Received: 26.09.1994
Revised: 10.10.1997
English version:
Theory of Probability and its Applications, 2000, Volume 44, Issue 1, Pages 1–17
DOI: https://doi.org/10.1137/S0040585X97977318
Bibliographic databases:
Language: Russian
Citation: V. I. Bakhtin, “Cramér asymptotics in a system with slow and fast Markovian motions”, Teor. Veroyatnost. i Primenen., 44:1 (1999), 14–33; Theory Probab. Appl., 44:1 (2000), 1–17
Citation in format AMSBIB
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\by V.~I.~Bakhtin
\paper Cram\'er asymptotics in a~system with slow and fast Markovian motions
\jour Teor. Veroyatnost. i Primenen.
\yr 1999
\vol 44
\issue 1
\pages 14--33
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\zmath{https://zbmath.org/?q=an:0963.60025}
\transl
\jour Theory Probab. Appl.
\yr 2000
\vol 44
\issue 1
\pages 1--17
\crossref{https://doi.org/10.1137/S0040585X97977318}
\isi{https://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=Publons&SrcAuth=Publons_CEL&DestLinkType=FullRecord&DestApp=WOS_CPL&KeyUT=000087555000001}
Linking options:
  • https://www.mathnet.ru/eng/tvp595
  • https://doi.org/10.4213/tvp595
  • https://www.mathnet.ru/eng/tvp/v44/i1/p14
    • This publication is cited in the following 6 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    		Теория вероятностей и ее применения Theory of Probability and its Applications
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