Convolution tail equivalent distributions: basic properties
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If you have a question about this talk, please contact Neil Walton.
The talk discusses the tail behaviour of 2fold convolutions $\overline{F \star F}$ of rightunbounded distributions and to the tail
behaviour of the distribution of the random sum $S_\tau$. We start with
the description of all possible values of the limit of the ratio
$\overline{F \star F}(x)/\overline F(x)$ as $x\to\infty$. This problem is
closely related to the problem of the lower limit of this ratio and goes
back to W. Rudin. The second part of the talk is devoted to conditions
under which $P(S_\tau>x)\sim E\tau \overline F(x)$ as $x\to\infty$. We
also consider applications of results obtained to random walks, compound
Poisson distributions, infinitely divisible laws, and branching processes.
This talk is part of the Optimization and Incentives Seminar series.
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