Moment convergence in renewal theory

A. Iksanov, A. Marynych, M. Meiners

Onderzoeksoutput: Boek/rapportRapportAcademic


Let ¿1, ¿2, . . . be independent copies of a positive random variable ¿, and let Sk := ¿ 1 + . . . + ¿ k, k ¿ N0. Define N(t) := #{k ¿ N0 : Sk= t}. (N(t))t=0 is a renewal counting process. It is known that if ¿ is in the domain of attraction of a stable law of index a ¿ (1, 2], then N(t), suitably shifted and scaled, converges in distribution as t ¿ 8 to a random variable with a stable law. We show that in this situation, also the first absolute moments converge to the first absolute moment of the limiting random variable. Further, the corresponding result for subordinators is established.
Originele taal-2Engels
Aantal pagina's7
StatusGepubliceerd - 2012

Publicatie series
Volume1208.3964 [math.PR]


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