The class $\mathscr{J}$ of subexponential distributions is characterized by $F(0) = 0, 1 - F^{(2)} (x) \sim 2\{1 - F(x)\}$ as $x \rightarrow \infty$. New properties of the class $\mathscr{J}$ are derived as well as for the more general case where $1 - F^{(2)} (x) \sim \beta\{1 - F(x)\}$. An application to transient renewal theory illustrates these results as does an adaptation of a result of Greenwood on randomly stopped sums of subexponentially distributed random variables.
Publié le : 1975-12-14
Classification:
Subexponential distributions,
regular variation,
renewal theory,
branching process,
random sum,
60E05,
60G40
@article{1176996225,
author = {Teugels, Jozef L.},
title = {The Class of Subexponential Distributions},
journal = {Ann. Probab.},
volume = {3},
number = {6},
year = {1975},
pages = { 1000-1011},
language = {en},
url = {http://dml.mathdoc.fr/item/1176996225}
}
Teugels, Jozef L. The Class of Subexponential Distributions. Ann. Probab., Tome 3 (1975) no. 6, pp. 1000-1011. http://gdmltest.u-ga.fr/item/1176996225/