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

Denis Denisov; Serguei Foss; Dmitry Korshunov

doi:10.3150/07-BEJ111

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

Denis Denisov, Serguei Foss, Dmitry Korshunov

Research output: Contribution to journal › Article › peer-review

17 Citations (Scopus)

Abstract

For a distribution F^*t of a random sum S_t = ?₁ + ... + ?_t of i.i.d, random variables with a common distribution F on the half-line [0, 8), we study the limits of the ratios of tails F^*t (x)/F (x) as x ? 8 (here, t is a counting random variable which does not depend on {? _n}_n= 1). We also consider applications of the results obtained to random walks, compound Poisson distributions, infinitely divisible laws, and subcritical branching processes. © 2008 ISI/BS.

Original language	English
Pages (from-to)	391-404
Number of pages	14
Journal	Bernoulli
Volume	14
Issue number	2
DOIs	https://doi.org/10.3150/07-BEJ111
Publication status	Published - May 2008

Keywords

Convolution equivalence
Convolution tail
Lower limit
Randomly stopped sums
Subexponential distribution

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AU - Denisov, Denis

AU - Foss, Serguei

AU - Korshunov, Dmitry

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N2 - For a distribution F*t of a random sum St = ?1 + ... + ?t of i.i.d, random variables with a common distribution F on the half-line [0, 8), we study the limits of the ratios of tails F*t (x)/F (x) as x ? 8 (here, t is a counting random variable which does not depend on {? n}n= 1). We also consider applications of the results obtained to random walks, compound Poisson distributions, infinitely divisible laws, and subcritical branching processes. © 2008 ISI/BS.

AB - For a distribution F*t of a random sum St = ?1 + ... + ?t of i.i.d, random variables with a common distribution F on the half-line [0, 8), we study the limits of the ratios of tails F*t (x)/F (x) as x ? 8 (here, t is a counting random variable which does not depend on {? n}n= 1). We also consider applications of the results obtained to random walks, compound Poisson distributions, infinitely divisible laws, and subcritical branching processes. © 2008 ISI/BS.

KW - Convolution equivalence

KW - Convolution tail

KW - Lower limit

KW - Randomly stopped sums

KW - Subexponential distribution

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VL - 14

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JO - Bernoulli

JF - Bernoulli

IS - 2

ER -

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

Abstract

Keywords

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