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Probl. Peredachi Inf., 2010, Volume 46, Issue 2, Pages 66–90 (Mi ppi2016)  

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

Large Systems

Large deviations for distributions of sums of random variables: Markov chain method

V. R. Fatalov

M. V. Lomonosov Moscow State University, Faculty of Mechanics and Mathematics

Abstract: Let $\{\xi_k\}_{k=0}^\infty$ be a sequence of i.i.d. real-valued random variables, and let $g(x)$ be a continuous positive function. Under rather general conditions, we prove results on sharp asymptotics of the probabilities $\mathbf P\{\frac1n\sum_{k=0}^{n-1}g(\xi_k)<d\}$, $n\to\infty$, and also of their conditional versions. The results are obtained using a new method developed in the paper, namely, the Laplace method for sojourn times of discrete-time Markov chains. We consider two examples: standard Gaussian random variables with $g(x)=x^p$, $p>0$, and exponential random variables with $g(x)=x$ for $x\ge0$.

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English version:
Problems of Information Transmission, 2010, 46:2, 160–183

Bibliographic databases:

UDC: 621.391.1+519.2
Received: 01.07.2008
Revised: 11.12.2009

Citation: V. R. Fatalov, “Large deviations for distributions of sums of random variables: Markov chain method”, Probl. Peredachi Inf., 46:2 (2010), 66–90; Problems Inform. Transmission, 46:2 (2010), 160–183

Citation in format AMSBIB
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\by V.~R.~Fatalov
\paper Large deviations for distributions of sums of random variables: Markov chain method
\jour Probl. Peredachi Inf.
\yr 2010
\vol 46
\issue 2
\pages 66--90
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\transl
\jour Problems Inform. Transmission
\yr 2010
\vol 46
\issue 2
\pages 160--183
\crossref{https://doi.org/10.1134/S0032946010020055}
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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. V. R. Fatalov, “Exact asymptotics of probabilities of large deviations for Markov chains: the Laplace method”, Izv. Math., 75:4 (2011), 837–868  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib  elib
    2. V. R. Fatalov, “Ergodic means for large values of $T$ and exact asymptotics of small deviations for a multi-dimensional Wiener process”, Izv. Math., 77:6 (2013), 1224–1259  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib  elib
    3. Kasparaviciute A., Deltuviene D., “Asymptotic Expansion For the Distribution Density Function of the Compound Poisson Process in Large Deviations”, J. Theor. Probab., 30:4 (2017), 1655–1676  crossref  mathscinet  zmath  isi  scopus
  • Проблемы передачи информации Problems of Information Transmission
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