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Sibirskie Èlektronnye Matematicheskie Izvestiya [Siberian Electronic Mathematical Reports], 2019, Volume 16, Pages 1464–1477
DOI: https://doi.org/10.33048/semi.2019.16.101
(Mi semr1142)
 

This article is cited in 9 scientific papers (total in 9 papers)

Probability theory and mathematical statistics

Large deviation principle for multidimensional first compound renewal processes in the phase space

A. A. Mogulskiiab, E. I. Prokopenkoba

a Sobolev Institute of Mathematics, 4, Koptyuga ave., Novosibirsk, 630090, Russia
b Novosibirsk State University, 1, Pirogova str., Novosibirsk, 630090, Russia
Full-text PDF (202 kB) Citations (9)
References:
Abstract: We obtain the large deviation principles for multidimensional first compound renewal processes $\mathbf{Z}(t)$ in the phase space $\mathbb{R}^d$, for this we find and investigate the rate function $D_Z(\alpha)$. Also we find asymptotics for the Laplace transform of this process when the time goes to infinity, for this we find and investigate the so-called fundamental function $A_Z(\mu)$.
Keywords: compound multidimensional renewal process, large deviations, renewal measure, Cramer's condition, deviation (rate) function, second deviation (rate) function, fundamental function.
Funding agency Grant number
Russian Science Foundation 18-11-00129
Received June 4, 2019, published October 17, 2019
Bibliographic databases:
Document Type: Article
UDC: 519.21
MSC: 60K05, 60F10
Language: Russian
Citation: A. A. Mogulskii, E. I. Prokopenko, “Large deviation principle for multidimensional first compound renewal processes in the phase space”, Sib. Èlektron. Mat. Izv., 16 (2019), 1464–1477
Citation in format AMSBIB
\Bibitem{MogPro19}
\by A.~A.~Mogulskii, E.~I.~Prokopenko
\paper Large deviation principle for multidimensional first compound renewal processes in the phase space
\jour Sib. \`Elektron. Mat. Izv.
\yr 2019
\vol 16
\pages 1464--1477
\mathnet{http://mi.mathnet.ru/semr1142}
\crossref{https://doi.org/10.33048/semi.2019.16.101}
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  • This publication is cited in the following 9 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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