From moment explosion to the asymptotic behavior of the cumulative distribution for a random variable

S. M. Aly

Uppsala University, Department of Mathematics

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.

Received: 22.05.2015

Language: English

DOI: 10.4213/tvp5070

 English version: Theory of Probability and its Applications, 2017, 61:3, 357–374

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