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Sibirskie Èlektronnye Matematicheskie Izvestiya [Siberian Electronic Mathematical Reports], 2019, Volume 16, Pages 1449–1463
DOI: https://doi.org/10.33048/semi.2019.19.100 (Mi semr1141) 		 
This article is cited in 9 scientific papers (total in 9 papers)

Probability theory and mathematical statistics

The rate function and the fundamental function for multidimensional compound renewal process

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
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DOI: https://doi.org/10.33048/semi.2019.19.100
Abstract: We consider two multidimensional compound renewal processes $\mathbf{Z}(t)$ and $\mathbf{Y}(t)$. Assuming that the increments satisfy the Cramer's condition, we define and investigate the rate functions and the fundamental functions for the processes $\mathbf{Z}(t)$ and $\mathbf{Y}(t)$.
Keywords: compound multidimensional renewal process, large deviations, Cramer's condition, deviation (rate) function, fundamental function, Legendre transformation.
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, “The rate function and the fundamental function for multidimensional compound renewal process”, Sib. Èlektron. Mat. Izv., 16 (2019), 1449–1463
Citation in format AMSBIB
\Bibitem{MogPro19}
\by A.~A.~Mogulskii, E.~I.~Prokopenko
\paper The rate function and the fundamental function for multidimensional compound renewal process
\jour Sib. \`Elektron. Mat. Izv.
\yr 2019
\vol 16
\pages 1449--1463
\mathnet{http://mi.mathnet.ru/semr1141}
\crossref{https://doi.org/10.33048/semi.2019.19.100}
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