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arXiv · 1303.4709

Asymptotics for sums of random variables with local subexponential behaviour

S. Asmussen·S. Foss·D. Korshunov
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Abstract

We study distributions $F$ on $[0,\infty)$ such that for some $T\le\infty$, $F^{*2}(x,x+T]\sim 2 F(x,x+T]$. The case $T=\infty$ corresponds to $F$ being subexponential, and our analysis shows that the properties for $T<\infty$ are, in fact, very similar to this classical case. A parallel theory is developed in the presence of densities. Applications are given to random walks, the key renewal theorem, compound Poisson process and Bellman-Harris branching processes.

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S. Asmussen, S. Foss, D. Korshunov. 2013-03-19. Asymptotics for sums of random variables with local subexponential behaviour. https://arxiv.org/abs/1303.4709

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