CHINESE JOURNAL OF APPLIED PROBABILITY AND STATIST 2010, 26(5) 469-476 DOI:      ISSN: 1001-4268 CN: 31-1256

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Equivalent Conditions for a Type of Convolution Closure
of Local Subexponential Distributions and Applications

Yu Changjun,Wang Yuebao

Department of Mathematics, Soochow University,

Abstract��

This paper obtains some equivelent conditions
for a type of convolution closure of local subexponential
distributions on $[0,\infty)$, which are also valid for
distributions on $(-\infty,\infty)$ under certain conditions. On the
basis of these results, the local asymptotics for the distribution
of symmetrization are given. The results above include the
corresponding, non-local results of Embrechts and Goldie
(1980)\ucite{1} and Geluk (2004)\ucite{2}. Some of our proofs are
more simple than those of Geluk (2004)\ucite{2}.

Keywords��