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Sibirsk. Mat. Zh., 2013, Volume 54, Number 2, Pages 286–297 (Mi smj2420)  

This article is cited in 7 scientific papers (total in 7 papers)

Inequalities and principles of large deviations for the trajectories of processes with independent increments

A. A. Borovkov, A. A. Mogul'skiĭ

Sobolev Institute of Mathematics, Novosibirsk, Russia

Abstract: We consider a homogeneous process $S(t)$ on $[0,\infty)$ with independent increments, establish the local and ordinary large deviation principles for the trajectories of the processes $s_T(t):=\frac1TS(tT)$, $t\in[0,1]$, as $T\to\infty$, and obtain a series of inequalities for the distributions of the trajectories of $S(t)$.

Keywords: process with independent increments, Cramer's condition, function of deviations, large deviation principle (LDP), local large deviation principle (local LDP), Chebyshev-type inequality, convex set.

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English version:
Siberian Mathematical Journal, 2013, 54:2, 217–226

Bibliographic databases:

UDC: 519.21
Received: 15.06.2012

Citation: A. A. Borovkov, A. A. Mogul'skiǐ, “Inequalities and principles of large deviations for the trajectories of processes with independent increments”, Sibirsk. Mat. Zh., 54:2 (2013), 286–297; Siberian Math. J., 54:2 (2013), 217–226

Citation in format AMSBIB
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\by A.~A.~Borovkov, A.~A.~Mogul'ski{\v\i}
\paper Inequalities and principles of large deviations for the trajectories of processes with independent increments
\jour Sibirsk. Mat. Zh.
\yr 2013
\vol 54
\issue 2
\pages 286--297
\mathnet{http://mi.mathnet.ru/smj2420}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=3088596}
\transl
\jour Siberian Math. J.
\yr 2013
\vol 54
\issue 2
\pages 217--226
\crossref{https://doi.org/10.1134/S0037446613020055}
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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. Mogulskii A., Pechersky E., Yambartsev A., “Large Deviations For Excursions of Non-Homogeneous Markov Processes”, Electron. Commun. Probab., 19 (2014), 1–8  crossref  mathscinet  isi  scopus
    2. 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
    3. A. A. Mogul'skiǐ, “The large deviation principle for a compound Poisson process”, Siberian Adv. Math., 27:3 (2017), 160–186  mathnet  crossref  crossref  elib
    4. A. A. Mogul'skiǐ, “The extended large deviation principle for a process with independent increments”, Siberian Math. J., 58:3 (2017), 515–524  mathnet  crossref  crossref  isi  elib  elib
    5. N. D. Vvedenskaya, A. V. Logachov, Yu. M. Suhov, A. A. Yambartsev, “A local large deviation principle for inhomogeneous birth-death processes”, Problems Inform. Transmission, 54:3 (2018), 263–280  mathnet  crossref  isi  elib
    6. F. C. Klebaner, A. V. Logachov, A. A. Mogulskii, “Extended large deviation principle for trajectories of processes with independent and stationary increments on the half-line”, Problems Inform. Transmission, 56:1 (2020), 56–72  mathnet  crossref  crossref  isi  elib
    7. A. V. Logachov, Y. M. Suhov, N. D. Vvedenskaya, A. A. Yambartsev, “A remark on normalizations in a local large deviations principle for inhomogeneous birth – and – death process”, Sib. elektron. matem. izv., 17 (2020), 1258–1269  mathnet  crossref
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