On lower limits and equivalences for distribution tails of randomly stopped sums

Denisov, Denis, Foss, S. and Korshunov, D. 2008. On lower limits and equivalences for distribution tails of randomly stopped sums. Bernoulli -London- 14 (2) , pp. 391-404. 10.3150/07-BEJ111

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Abstract

For a distribution F*τ of a random sum Sτ=ξ1+⋯+ξτ of i.i.d. random variables with a common distribution F on the half-line [0, ∞), we study the limits of the ratios of tails as x→∞ (here, τ is a counting random variable which does not depend on {ξn}n≥1). We also consider applications of the results obtained to random walks, compound Poisson distributions, infinitely divisible laws, and subcritical branching processes.

Item Type:	Article
Date Type:	Publication
Status:	Published
Schools:	Mathematics
Subjects:	Q Science > QA Mathematics
Uncontrolled Keywords:	convolution tail; convolution equivalence; lower limit; randomly stopped sums; subexponential distribution
Additional Information:	Pdf uploaded in accordance with publisher's policy at http://www.sherpa.ac.uk/romeo/issn/1350-7265/ (accessed 25/02/2014)
Publisher:	Bernoulli Society for Mathematical Statistics and Probability
ISSN:	1350-7265
Date of First Compliant Deposit:	30 March 2016
Last Modified:	04 May 2023 19:21
URI:	https://orca.cardiff.ac.uk/id/eprint/13512

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