Authors
Søren Asmussen, Serguei Foss, Dmitry Korshunov
Publication date
2003/4/21
Journal
Journal of Theoretical Probability
Volume
16
Issue
2
Pages
489-518
Publisher
Springer Netherlands
Description
We study distributions F on [0,∞) such that for some T ≤ ∞, F *2(x, x+T] ∼ 2F(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.
Total citations
Scholar articles
S Asmussen, S Foss, D Korshunov - Journal of Theoretical Probability, 2003