## 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

#### Abstract

For a distribution *F*^{*τ} of a random sum *S*_{τ}=*ξ*_{1}+⋯+*ξ*_{τ} 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 {*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.

#### 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.