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

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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. Mogulskii^ab, E. I. Prokopenko^ba

^a Sobolev Institute of Mathematics, 4, Koptyuga ave., Novosibirsk, 630090, Russia
^b Novosibirsk State University, 1, Pirogova str., Novosibirsk, 630090, Russia

Full-text PDF (198 kB) Citations (9)

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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}

Linking options:

https://www.mathnet.ru/eng/semr1141

https://www.mathnet.ru/eng/semr/v16/p1449

This publication is cited in the following 9 articles:

A. V. Logachov, A. A. Mogulskii, E. I. Prokopenko, “Large deviation principle for terminating multidimensional compound renewal processes with application to polymer pinning models”, Problems Inform. Transmission, 58:2 (2022), 144–159
A. V. Logachov, A. A. Mogul'skii, “Large deviation principles for the processes admitting embedded compound renewal processes”, Siberian Math. J., 63:1 (2022), 119–137
T. Konstantopoulos, A. V. Logachov, A. A. Mogulskii, S. G. Foss, “Limit theorems for the maximal path weight in a directed graph on the line with random weights of edges”, Problems Inform. Transmission, 57:2 (2021), 161–177
A. Logachov, A. Mogulskii, E. Prokopenko, A. Yambartsev, “Local theorems for (multidimensional) additive functionals of semi-Markov chains”, Stoch. Process. Their Appl., 137 (2021), 149–166
A. A. Mogulskii, E. I. Prokopenko, “Printsip bolshikh uklonenii dlya konechnomernykh raspredelenii mnogomernykh obobschennykh protsessov vosstanovleniya”, Matem. tr., 23:2 (2020), 148–176
A. A. Mogul'skii, A. V. Logachov, “Local Theorems For Finite-Dimensional Increments of Compound Multidimensional Arithmetic Renewal Processes With Light Tails”, Sib. Electron. Math. Rep., 17 (2020), 1766–1786
A. A. Mogul'skiǐ, E. I. Prokopenko, “Local theorems for arithmetic multidimensional compound renewal processes under Cramér's condition”, Siberian Adv. Math., 30:4 (2020), 284–302
A. A. Mogulskii, E. I. Prokopenko, “Printsip bolshikh uklonenii v fazovom prostranstve dlya mnogomernogo pervogo obobschennogo protsessa vosstanovleniya”, Sib. elektron. matem. izv., 16 (2019), 1464–1477
A. A. Mogulskii, E. I. Prokopenko, “Printsip bolshikh uklonenii v fazovom prostranstve dlya mnogomernogo vtorogo obobschennogo protsessa vosstanovleniya”, Sib. elektron. matem. izv., 16 (2019), 1478–1492

Citing articles in Google Scholar: Russian citations, English citations
Related articles in Google Scholar: Russian articles, English articles

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