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Sibirsk. Mat. Zh., 2016, Volume 57, Number 3, Pages 562–595 (Mi smj2764)  

This article is cited in 3 scientific papers (total in 3 papers)

Large deviation principles in boundary problems for compound renewal processes

A. A. Borovkovab

a Novosibirsk State University, Novosibirsk, Russia
b Sobolev Institute of Mathematics, Siberian Branch of the Russian Academy of Sciences, Novosibirsk, Russia

Abstract: We find explicit logarithmic asymptotics for the probability of events related to the intersection (or nonintersection) of arbitrary remote boundaries by the trajectory of a compound renewal process.

Keywords: compound renewal process, large deviation principle, boundary problem, second deviation function, admissible nonhomogeneity, regular deviation, shortest trajectory, first boundary problem, level curves, second boundary problem.

Funding Agency Grant Number
Russian Foundation for Basic Research 14-01-00220
The author was supported by the Russian Foundation for Basic Research (Grant 14-01-00220).


DOI: https://doi.org/10.17377/smzh.2016.57.306

Full text: PDF file (622 kB)
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English version:
Siberian Mathematical Journal, 2016, 57:3, 442–469

Bibliographic databases:

Document Type: Article
UDC: 519.21
Received: 22.01.2015

Citation: A. A. Borovkov, “Large deviation principles in boundary problems for compound renewal processes”, Sibirsk. Mat. Zh., 57:3 (2016), 562–595; Siberian Math. J., 57:3 (2016), 442–469

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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. A. A. Mogul'skiǐ, “On a property of the Legendre transform”, Siberian Adv. Math., 28:1 (2018), 65–73  mathnet  crossref  crossref  elib
    2. A. A. Borovkov, A. A. Mogulskii, “Integro-local limit theorems for compound renewal processes under Cramér's condition. I”, Siberian Math. J., 59:3 (2018), 383–402  mathnet  crossref  crossref  isi  elib
    3. A. A. Mogulskii, “Lokalnye teoremy dlya arifmeticheskikh obobschennykh protsessov vosstanovleniya pri vypolnenii usloviya Kramera”, Sib. elektron. matem. izv., 16 (2019), 21–41  mathnet  crossref
  • Сибирский математический журнал Siberian Mathematical Journal
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