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 Teor. Veroyatnost. i Primenen.: Year: Volume: Issue: Page: Find

 Teor. Veroyatnost. i Primenen., 1979, Volume 24, Issue 4, Pages 673–691 (Mi tvp2890)

Rough limit theorems on large deviations for Markov stochastic processes. III

A. D. Wentzell

Moscow

Abstract: This is the continuation of the papers [8], [9]. In [9] some rough limit theorems were deduced from the estimates of [8]. These theorems are analogous to the limit theorems for the sums of independent random variables concerning «very large» deviations of order $\sqrt n$. In the present paper rough limit theorems for some other classes of families of Markov processes are derived from the estimates of [8] (slighthly modified); some of them are analogous to limit theorems concerning «not very large» deviations (those of order $o(\sqrt n)$ for the sums of independent random variables.

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English version:
Theory of Probability and its Applications, 1980, 24:4, 675–692

Bibliographic databases:

Citation: A. D. Wentzell, “Rough limit theorems on large deviations for Markov stochastic processes. III”, Teor. Veroyatnost. i Primenen., 24:4 (1979), 673–691; Theory Probab. Appl., 24:4 (1980), 675–692

Citation in format AMSBIB
\Bibitem{Ven79} \by A.~D.~Wentzell \paper Rough limit theorems on large deviations for Markov stochastic processes.~III \jour Teor. Veroyatnost. i Primenen. \yr 1979 \vol 24 \issue 4 \pages 673--691 \mathnet{http://mi.mathnet.ru/tvp2890} \mathscinet{http://www.ams.org/mathscinet-getitem?mr=550526} \zmath{https://zbmath.org/?q=an:0447.60024} \transl \jour Theory Probab. Appl. \yr 1980 \vol 24 \issue 4 \pages 675--692 \crossref{https://doi.org/10.1137/1124083} \isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=A1979KW11900001} 

• http://mi.mathnet.ru/eng/tvp2890
• http://mi.mathnet.ru/eng/tvp/v24/i4/p673

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This publication is cited in the following articles:
1. A. A. Borovkov, “Boundary-value problems, the invariance principle, and large deviations”, Russian Math. Surveys, 38:4 (1983), 259–290
2. V. I. Piterbarg, V. R. Fatalov, “The Laplace method for probability measures in Banach spaces”, Russian Math. Surveys, 50:6 (1995), 1151–1239