Lower Limits for Distribution Tails of Randomly Stopped Sums
Lower Limits for Distribution Tails of Randomly Stopped Sums
We study lower limits for the ratio $\overline{F^{*\tau}}(x)/\,\overline F(x)$ of tail distributions, where $F^{*\tau}$ is a distribution of a sum of a random size $\tau$ of independent identically distributed random variables having a common distribution F, and a random variable $\tau$ does not depend on the summands.