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Matematicheskie Trudy, 2014, Volume 17, Number 2, Pages 84–101 (Mi mt278)  
This article is cited in 5 scientific papers (total in 5 papers)

Large deviation principles for sums of random vectors and the corresponding renewal functions in the inhomogeneous case

A. A. Borovkovab, A. A. Mogul'skiĭba

a Novosibirsk State University, Novosibirsk, 630090 Russia
b Sobolev Institute of Mathematics, Novosibirsk, 630090 Russia
Full-text PDF (245 kB) Citations (5)
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Abstract: Under the inhomogeneous case wemean the case when one or several (arbitrarily many) inhomogeneous summands are added to the sum of independent identically distributed vectors. We find necessary and sufficient conditions under which the large deviation principles for such sums and the corresponding renewal functions have the same form that in the homogeneous case.
Key words: large deviation principles, inhomogeneous sum of random vectors, renewal function, deviation rate function, second deviation rate function.
Received: 24.06.2014
English version:
Siberian Advances in Mathematics, 2015, Volume 25, Issue 4, Pages 255–267
DOI: https://doi.org/10.3103/S1055134415040033
Bibliographic databases:
Document Type: Article
UDC: 519.21
Language: Russian
Citation: A. A. Borovkov, A. A. Mogul'skiǐ, “Large deviation principles for sums of random vectors and the corresponding renewal functions in the inhomogeneous case”, Mat. Tr., 17:2 (2014), 84–101; Siberian Adv. Math., 25:4 (2015), 255–267
Citation in format AMSBIB
\Bibitem{BorMog14}
\by A.~A.~Borovkov, A.~A.~Mogul'ski{\v\i}
\paper Large deviation principles for sums of random vectors and the corresponding renewal functions in the inhomogeneous case
\jour Mat. Tr.
\yr 2014
\vol 17
\issue 2
\pages 84--101
\mathnet{http://mi.mathnet.ru/mt278}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=3330052}
\transl
\jour Siberian Adv. Math.
\yr 2015
\vol 25
\issue 4
\pages 255--267
\crossref{https://doi.org/10.3103/S1055134415040033}
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  • https://www.mathnet.ru/eng/mt278
  • https://www.mathnet.ru/eng/mt/v17/i2/p84
    • This publication is cited in the following 5 articles:
    1. A. A. Borovkov, “On Large Deviation Principles for Compound Renewal Processes”, Math. Notes, 106:6 (2019), 864–871  mathnet  crossref  crossref  mathscinet  isi  elib
    2. Alexander Veretennikov, Springer Proceedings in Mathematics & Statistics, 208, Modern Problems of Stochastic Analysis and Statistics, 2017, 457  crossref
    3. A. A. Borovkov, “Large deviation principles in boundary problems for compound renewal processes”, Siberian Math. J., 57:3 (2016), 442–469  mathnet  crossref  crossref  mathscinet  isi  elib  elib
    4. A. A. Borovkov, A. A. Mogul'skiǐ, “Large deviation principles for the finite-dimensional distributions of compound renewal processes”, Siberian Math. J., 56:1 (2015), 28–53  mathnet  crossref  mathscinet  isi  elib  elib
    5. A. A. Borovkov, A. A. Mogul'skii, “Large deviation principles for trajectories of compound renewal processes. I”, Theory Probab. Appl., 60:2 (2016), 207–221  mathnet  crossref  crossref  mathscinet  isi  elib
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    		Математические труды Siberian Advances in Mathematics
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