Asymptotics for sums of random variables with local subexponential behaviour

الأصل · EN

We study distributions F on [0,∞) such that for some T≤∞, F*²(x,x+T] 2 F(x,x+T]. The case T=∞ corresponds to F being subexponential, and our analysis shows that the properties for T<∞ 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.