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SECOND ORDER SUBEXPONENTIALITY AND INFINITE DIVISIBILITY

Part of: Distribution theory - Probability Stochastic processes

Published online by Cambridge University Press:  22 June 2020

TOSHIRO WATANABE Open the ORCID record for TOSHIRO WATANABE [Opens in a new window]
TOSHIRO WATANABE*
Affiliation:
Center for Mathematical Sciences,The University of Aizu, Aizu-Wakamatsu, Fukushima965-8580, Japan
*
e-mail: markov2000t@yahoo.co.jp
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Abstract

We characterize the second order subexponentiality of an infinitely divisible distribution on the real line under an exponential moment assumption. We investigate the asymptotic behaviour of the difference between the tails of an infinitely divisible distribution and its Lévy measure. Moreover, we study the second order asymptotic behaviour of the tail of the $t$th convolution power of an infinitely divisible distribution. The density version for a self-decomposable distribution on the real line without an exponential moment assumption is also given. Finally, the regularly varying case for a self-decomposable distribution on the half line is discussed.

Keywords

second order subexponentialitylocal subexponentialityinfinite divisibility

MSC classification

Primary: 60E07: Infinitely divisible distributions; stable distributions
Secondary: 60G50: Sums of independent random variables; random walks 60G51: Processes with independent increments; L'evy processes
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 112 , Issue 3 , June 2022 , pp. 367 - 390
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Copyright
© 2020 Australian Mathematical Publishing Association Inc.

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Footnotes

Communicated by N. Ross

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