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

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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 F*τ (x)/F (x) as x → ∞ (here, τ is a counting random variable which does not depend on {ξ 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	13
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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title = "On lower limits and equivalences for distribution tails of randomly stopped sums",

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 F*τ (x)/F (x) as x → ∞ (here, τ is a counting random variable which does not depend on {ξ n}n≥ 1). We also consider applications of the results obtained to random walks, compound Poisson distributions, infinitely divisible laws, and subcritical branching processes. {\textcopyright} 2008 ISI/BS.",

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AU - Denisov, Denis

AU - Foss, Serguei

AU - Korshunov, Dmitry

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N2 - 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 F*τ (x)/F (x) as x → ∞ (here, τ is a counting random variable which does not depend on {ξ 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*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 F*τ (x)/F (x) as x → ∞ (here, τ is a counting random variable which does not depend on {ξ 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

U2 - 10.3150/07-BEJ111

DO - 10.3150/07-BEJ111

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VL - 14

SP - 391

EP - 404

JO - Bernoulli

JF - Bernoulli

IS - 2

ER -

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

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Keywords

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