ON THE ASYMPTOTIC-BEHAVIOR OF THE HARMONIC RENEWAL MEASURE

Authors
SGIBNEV MS
Citation
Ms. Sgibnev, ON THE ASYMPTOTIC-BEHAVIOR OF THE HARMONIC RENEWAL MEASURE, Journal of theoretical probability, 11(2), 1998, pp. 371-382
Citations number
30
Categorie Soggetti
Statistic & Probability","Statistic & Probability
Journal title
Journal of theoretical probability → ACNP
ISSN journal
08949840
Volume
11
Issue
2
Year of publication
1998
Pages
371 - 382
Database
ISI
SICI code
0894-9840(1998)11:2<371:OTAOTH>2.0.ZU;2-F
Abstract
We study the tail behavior of the harmonic renewal measure U = Sigma(n =1)(infinity) (1/n) F-n, where F is a probability distribution with f inite negative mean and F-n is the n-fold convolution of F. As an app lication of the obtained result on U, we give alternative proofs of so me known results concerning the tail behavior of the supremum and the first positive sum of a random walk with negative drift.