×

zbMATH — the first resource for mathematics

Asymptotics for sums of random variables with local subexponential behaviour. (English) Zbl 1033.60053
This paper studies distributions \(F\) on \([0,\,\infty)\) such that for some \(T\leq\infty\), \(F^{*2}(x,\,x+T]\sim 2F(x,\,x+T]\). 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.

MSC:
60G50 Sums of independent random variables; random walks
60E05 Probability distributions: general theory
PDF BibTeX XML Cite
Full Text: DOI