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Short Communications

Second-order asymptotic behavior of subexponential infinitely divisible distributions

A. Baltrūnas^a, A. L. Yakymiv<sup>b

a</sup> Institute of Mathematics and Informatics
^b Steklov Mathematical Institute, Russian Academy of Sciences

Abstract: In this paper, a new way to obtain the rate of convergence for subexponential infinitely divisible distributions is proposed. Namely, for the subexponential infinitely divisible distribution function $H(x)$ with the Lévy measure $\mu ,$ the estimate of difference
$$ 1-H(x)-\mu((x,\infty)) $$
as $x\to\infty $ has been obtained.

Keywords: infinitely divisible distributions, Lévy measure, subexponential distributions, dominated variation, $RO$-varying functions.

Received: 30.01.2002

DOI: 10.4213/tvp257

 English version: Theory of Probability and its Applications, 2004, 48:4, 703–710

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