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 $\overline{F^{*\tau}}(x)/\overline{F}(x)$ 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.
Citation
Denis Denisov. Serguei Foss. Dmitry Korshunov. "On lower limits and equivalences for distribution tails of randomly stopped sums." Bernoulli 14 (2) 391 - 404, May 2008. https://doi.org/10.3150/07-BEJ111
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