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Sibirskie Èlektronnye Matematicheskie Izvestiya [Siberian Electronic Mathematical Reports], 2020, Volume 17, Pages 824–839
DOI: https://doi.org/10.33048/semi.2020.17.060 (Mi semr1254) 		 
Probability theory and mathematical statistics

Sharp asymptotics for the Laplace transform of the compound renewal process and related problems

A. A. Borovkov

Sobolev Institute of Mathematics, 4, Koptyuga ave., 630090, Novosibirsk, Russia
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DOI: https://doi.org/10.33048/semi.2020.17.060
Abstract: Sharp asymptotics for the Laplace transform of the compound renewal process (CRP) are found under the Cramer moment condition on the jumps of the process. This result allowed us to obtain asymptotic inequalities for the distribution of the maximum value of the CRP on increasing time intervals and also to find the asymptotic behavior of all the moments of the CRP. The asimptotics of the two first moments of CRP are found under conditions close to minimal ones.
Keywords: compound renewal process, Laplace transform, sharp asymptotics, distribution of the maximum of process, asymptotics of the moments.
Funding agency Grant number
Russian Foundation for Basic Research 18-01-00101_а
Siberian Branch of Russian Academy of Sciences I.1.3 (проект № 0314-2016-0008)
Received April 16, 2020, published June 25, 2020
Bibliographic databases:
Document Type: Article
UDC: 519.21
MSC: 60F10, 60K05
Language: Russian
Citation: A. A. Borovkov, “Sharp asymptotics for the Laplace transform of the compound renewal process and related problems”, Sib. Èlektron. Mat. Izv., 17 (2020), 824–839
Citation in format AMSBIB
\Bibitem{Bor20}
\by A.~A.~Borovkov
\paper Sharp asymptotics for the Laplace transform of the compound renewal process and related problems
\jour Sib. \`Elektron. Mat. Izv.
\yr 2020
\vol 17
\pages 824--839
\mathnet{http://mi.mathnet.ru/semr1254}
\crossref{https://doi.org/10.33048/semi.2020.17.060}
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