Convolution tail equivalent distributions: basic properties

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• Prof Dmitri Korshunov, (Novosibirsk)
• Friday 27 February 2009, 14:00-15:00
• MR12, CMS, Wilberforce Road, Cambridge, CB3 0WB.

If you have a question about this talk, please contact Neil Walton.

The talk discusses the tail behaviour of 2-fold convolutions $\overline{F \star F}$ of right-unbounded 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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