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Teoriya Veroyatnostei i ee Primeneniya, 2019, Volume 64, Issue 4, Pages 625–641
DOI: https://doi.org/10.4213/tvp5285 (Mi tvp5285) 		 
This article is cited in 8 scientific papers (total in 8 papers)

Properties of the deviation rate function and the asymptotics for the Laplace thansform of the distribution of a compound renewal process

A. A. Borovkov, A. A. Mogul'skii, E. I. Prokopenko

Sobolev Institute of Mathematics, Siberian Branch of the Russian Academy of Sciences, Novosibirsk
Full-text PDF (522 kB) Citations (8)
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DOI: https://doi.org/10.4213/tvp5285
Abstract: We find the asymptotics for the logarithm of the Laplace transform of the distribution of a compound renewal process as time increases unboundedly. It is assumed that the elements of the governing sequences of the renewal process satisfy Cramér's moment condition. Representations for the deviation rate function of the compound renewal process are found.
Keywords: compound renewal process, large deviations, large deviation principle, Cramér's condition, deviation rate function, Legendre transform, Laplace transform asymptotics.
Funding agency Grant number
Russian Foundation for Basic Research 18-01-00101
This research was carried out with the financial support of the Russian Foundation for Basic Research (grant 18-01-00101).
Received: 26.12.2018
Accepted: 12.02.2019
English version:
Theory of Probability and its Applications, 2020, Volume 64, Issue 4, Pages 499–512
DOI: https://doi.org/10.1137/S0040585X97T989660
Bibliographic databases:
Document Type: Article
Language: Russian
Citation: A. A. Borovkov, A. A. Mogul'skii, E. I. Prokopenko, “Properties of the deviation rate function and the asymptotics for the Laplace thansform of the distribution of a compound renewal process”, Teor. Veroyatnost. i Primenen., 64:4 (2019), 625–641; Theory Probab. Appl., 64:4 (2020), 499–512
Citation in format AMSBIB
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    • This publication is cited in the following 8 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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