Asymptotics for Sums of Random Variables with Local Subexponential Behaviour

By Søren Asmussen, Serguei Foss, Dmitry Korshunov. 2003

137 citations recorded by the source corpus.

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.

Subfields: Artificial Intelligence, Management Science and Operations Research, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/61c60659c0d0ce58b6aae38956db2ee3aa097ef3

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In Artificial Intelligence

In Management Science and Operations Research

In Mathematical Physics

Citations in the corpus

Conditional distribution of heavy tailed random variables on large deviations of their sum (2009, methodology): “This can be easily verified using the sufficient conditions for ∆-subexponentiality provided in [2].”
Local limits of conditioned Galton-Watson trees: the infinite spine case (2013, background): “Notice that (20) and (24) directly imply that the total progeny distribution enjoys the local sub-exponential property, see [3].”
Asymptotic Tail Probabilities of Sums of Dependent Subexponential Random Variables (2009, background): “[3], Geluk and De Vries [14], and Foss et al.”