Lower limits for distributions of randomly stopped sums

Denis Denisov; Sergey Foss; Dmitry Korshunov

Lower limits for distributions of randomly stopped sums

Probability 2017-11-29 v1

Authors: Denis Denisov , Sergey Foss , Dmitry Korshunov

Abstract

We study lower limits for the ratio $\frac{\bar{F^{*\tau}}(x)}{\bar F(x)}$ of tail distributions where $F^{*\tau}$ is a distribution of a sum of a random size $\tau$ of i.i.d. random variables having a common distribution $F$ , and a random variable $\tau$ does not depend on summands.

Keywords

heavy-tailed distributions

Cite

@article{arxiv.0711.4491,
  title  = {Lower limits for distributions of randomly stopped sums},
  author = {Denis Denisov and Sergey Foss and Dmitry Korshunov},
  journal= {arXiv preprint arXiv:0711.4491},
  year   = {2017}
}

Comments

This research is a continuation of arXiv:math/0510273 and arXiv:math/0701920. 11 pages

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