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Teoriya Veroyatnostei i ee Primeneniya, 2016, Volume 61, Issue 3, Pages 489–508
DOI: https://doi.org/10.4213/tvp5070 (Mi tvp5070) 		 
From moment explosion to the asymptotic behavior of the cumulative distribution for a random variable

S. M. Aly

Uppsala University, Department of Mathematics
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DOI: https://doi.org/10.4213/tvp5070
Abstract: We study the Tauberian relations between the moment generating function (MGF) and the complementary cumulative distribution function of a random variable whose MGF is finite only on part of the real line. We relate the right tail behavior of the cumulative distribution function of such a random variable to the behavior of its MGF near the critical moment. We apply our results to an arbitrary superposition of a CIR process and the time-integral of this process.
Keywords: regular variation, Tauberian theorems, moment generating function, tail asymptotic, CIR process.
Funding agency Grant number
Riksbankens Jubileumsfond P10-0113:1
This work was supported by a grant from Riksbankens Jubileumsfond (P10-0113:1).
Received: 22.05.2015
English version:
Theory of Probability and its Applications, 2017, Volume 61, Issue 3, Pages 357–374
DOI: https://doi.org/10.1137/S0040585X97T988228
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Document Type: Article
Language: English
Citation: S. M. Aly, “From moment explosion to the asymptotic behavior of the cumulative distribution for a random variable”, Teor. Veroyatnost. i Primenen., 61:3 (2016), 489–508; Theory Probab. Appl., 61:3 (2017), 357–374
Citation in format AMSBIB
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