D. É. Denisov, D. A. Korshunov, S. G. Foss, “Lower Limits for Distribution Tails of Randomly Stopped Sums”, Teor. Veroyatnost. i Primenen., 2007, Volume 52, Issue 4,Pages <nobr>794

This article is cited in 10 papers

Short Communications

Lower Limits for Distribution Tails of Randomly Stopped Sums

D. É. Denisov^a, D. A. Korshunov^b, S. G. Foss^a

^a Heriot Watt University
^b Sobolev Institute of Mathematics, Siberian Branch of the Russian Academy of Sciences

Abstract: We study lower limits for the ratio $\overline{F^{*\tau}}(x)/\,\overline F(x)$ of tail distributions, where $F^{*\tau}$ is a distribution of a sum of a random size $\tau$ of independent identically distributed random variables having a common distribution $F$, and a random variable $\tau$ does not depend on the summands.

Keywords: convolution tail, random sums of random variables, lower limit, heavy-tailed and light-tailed distributions.

Received: 13.06.2007

DOI: 10.4213/tvp1648