Bernoulli

  • Bernoulli
  • Volume 14, Number 2 (2008), 391-404.

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

Denis Denisov, Serguei Foss, and 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 $\overline{F^{*\tau}}(x)/\overline{F}(x)$ 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.

Article information

Source
Bernoulli Volume 14, Number 2 (2008), 391-404.

Dates
First available in Project Euclid: 22 April 2008

Permanent link to this document
https://projecteuclid.org/euclid.bj/1208872110

Digital Object Identifier
doi:10.3150/07-BEJ111

Mathematical Reviews number (MathSciNet)
MR2544093

Zentralblatt MATH identifier
1157.60315

Keywords
convolution tail convolution equivalence lower limit randomly stopped sums subexponential distribution

Citation

Denisov, Denis; Foss, Serguei; Korshunov, Dmitry. On lower limits and equivalences for distribution tails of randomly stopped sums. Bernoulli 14 (2008), no. 2, 391--404. doi:10.3150/07-BEJ111. https://projecteuclid.org/euclid.bj/1208872110.


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