Local Subexponentiality and Self-decomposability

Toshiro Watanabe () and Kouji Yamamuro ()
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Toshiro Watanabe: The University of Aizu
Kouji Yamamuro: Gifu University

Journal of Theoretical Probability, 2010, vol. 23, issue 4, 1039-1067

Abstract: Abstract The class of exponential tilts of convolution equivalent distributions is determined. As a corollary, the local subexponentiality of one-sided infinitely divisible distributions is characterized. It is applied to the subexponentiality of the densities of a self-decomposable distribution and its Lévy measure. Bondesson’s conjecture on the density of the Lévy measure of a lognormal distribution is solved as an example. Results of Denisov et al. on the distributions of random sums are extended to the two-sided case. Finally, the local subexponentiality of the distribution of the supremum of a random walk is characterized.

Keywords: Self-decomposability; Local subexponentiality; Infinite divisibility; Convolution equivalence; Supremum of a random walk; 60E07; 60G50 (search for similar items in EconPapers)
Date: 2010
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Citations: View citations in EconPapers (3)

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DOI: 10.1007/s10959-009-0240-8

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