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Matematicheskie Zametki, 2008, Volume 84, Issue 5, Pages 741–754
DOI: https://doi.org/10.4213/mzm6358 (Mi mzm6358) 		 
This article is cited in 3 scientific papers (total in 3 papers)

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
Full-text PDF (505 kB) Citations (3)
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DOI: https://doi.org/10.4213/mzm6358
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.
Received: 23.05.2007
English version:
Mathematical Notes, 2008, Volume 84, Issue 5, Pages 688–702
DOI: https://doi.org/10.1134/S0001434608110102
Bibliographic databases:
UDC: 519.21
Language: Russian
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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    • This publication is cited in the following 3 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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