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Mat. Zametki, 2008, Volume 84, Issue 5, Pages 741–754 (Mi mz6358)  

This article is cited in 1 scientific paper (total in 1 paper)

Formula for the Laplace Transform of the Projection of a Distribution on the Positive Semiaxis and Some of Its Applications

S. V. Nagaev

Sobolev Institute of Mathematics, Siberian Branch of the Russian Academy of Sciences

Abstract: We obtain a formula for the Laplace transform of the restriction of an arbitrary probability distribution on the positive semiaxis in the form of a Cauchy-type integral in infinite limits of the characteristic function of this distribution. Using this result and the estimates of the concentration function of the sum of independent random variables, we derive a representation for the Laplace transform of the restriction of the harmonic measure on the positive semiaxis. In conclusion, we present an estimate of the lower ladder height distribution for the case in which the distribution of the value of the jump in a random walk is normal.

Keywords: Laplace transform, probability distribution, Cauchy integral, harmonic measure, renewal measure, random walk, Vitali theorem

DOI: https://doi.org/10.4213/mzm6358

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English version:
Mathematical Notes, 2008, 84:5, 688–702

Bibliographic databases:

UDC: 519.21
Received: 23.05.2007

Citation: S. V. Nagaev, “Formula for the Laplace Transform of the Projection of a Distribution on the Positive Semiaxis and Some of Its Applications”, Mat. Zametki, 84:5 (2008), 741–754; Math. Notes, 84:5 (2008), 688–702

Citation in format AMSBIB
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\by S.~V.~Nagaev
\paper Formula for the Laplace Transform of the Projection of a Distribution on the Positive Semiaxis and Some of Its Applications
\jour Mat. Zametki
\yr 2008
\vol 84
\issue 5
\pages 741--754
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\crossref{https://doi.org/10.4213/mzm6358}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=2500640}
\transl
\jour Math. Notes
\yr 2008
\vol 84
\issue 5
\pages 688--702
\crossref{https://doi.org/10.1134/S0001434608110102}
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  • https://doi.org/10.4213/mzm6358
  • http://mi.mathnet.ru/eng/mz/v84/i5/p741

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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. S. V. Nagaev, “Exact expressions for the moments of ladder heights”, Siberian Math. J., 51:4 (2010), 675–695  mathnet  crossref  mathscinet  isi
  • Математические заметки Mathematical Notes
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