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Teoriya Veroyatnostei i ee Primeneniya, 2001, Volume 46, Issue 2, Pages 209–232
DOI: https://doi.org/10.4213/tvp3915 (Mi tvp3915) 		 
This article is cited in 29 scientific papers (total in 30 papers)

On Probabilities of Large Deviations for Random Walks. I. Regularly Varying Distribution Tails

A. A. Borovkova, K. A. Borovkovb

a Sobolev Institute of Mathematics, Siberian Branch of the Russian Academy of Sciences
b University of Melbourne, Department of Mathematics and Statistics
Full-text PDF (2155 kB) Citations (30)
DOI: https://doi.org/10.4213/tvp3915
Abstract: We establish first-order approximations and asymptotic expansions for probabilities of crossing arbitrary curvilinear boundaries in the large deviations range by random walks with regularly varying distribution tails. In particular, we study the large deviations probabilities for the sums and maxima of partial sums of independent and identically distributed random variables, including the asymptotic behavior of the densities when they exist. Extensions to the "regular exponential" case (when the distribution tail differs from the exponential one by a regularly varying factor) are considered in part II of the paper.
Keywords: large deviations, random walk, regular variation.
Received: 23.05.2000
English version:
Theory of Probability and its Applications, 2002, Volume 46, Issue 2, Pages 193–213
DOI: https://doi.org/10.1137/S0040585X97978877
Bibliographic databases:
Language: Russian
Citation: A. A. Borovkov, K. A. Borovkov, “On Probabilities of Large Deviations for Random Walks. I. Regularly Varying Distribution Tails”, Teor. Veroyatnost. i Primenen., 46:2 (2001), 209–232; Theory Probab. Appl., 46:2 (2002), 193–213
Citation in format AMSBIB
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\paper On Probabilities of Large Deviations for Random Walks. I. Regularly Varying Distribution Tails
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\pages 209--232
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\transl
\jour Theory Probab. Appl.
\yr 2002
\vol 46
\issue 2
\pages 193--213
\crossref{https://doi.org/10.1137/S0040585X97978877}
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  • https://www.mathnet.ru/eng/tvp/v46/i2/p209
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    This publication is cited in the following 30 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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    		Теория вероятностей и ее применения Theory of Probability and its Applications
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