Moment convergence in renewal theory

A. Iksanov, A. Marynych, M. Meiners

Research output: Book/ReportReportAcademic

Abstract

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.
Original languageEnglish
Publishers.n.
Number of pages7
Publication statusPublished - 2012

Publication series

NamearXiv.org
Volume1208.3964 [math.PR]

Fingerprint Dive into the research topics of 'Moment convergence in renewal theory'. Together they form a unique fingerprint.

Cite this