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A Collector's Problem with Renewal Arrival Processes

Part of:Limit theoremsSpecial processes

Published online by Cambridge University Press:  14 July 2016

Offer Kella and
Wolfgang Stadje
Offer Kella*
Affiliation:
The Hebrew University of Jerusalem
Wolfgang Stadje*
Affiliation:
University of Osnabrück
*
∗ Postal address: Department of Statistics, The Hebrew University of Jerusalem, Mount Scopus, Jerusalem, 91905, Israel. Email address: offer.kella@huji.ac.il
∗∗ Postal address: Department of Mathematics and Computer Science, University of Osnabrück, 49069 Osnabrück, Germany. Email address: wolfgang@mathematik.uni-osnabrueck.de
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Abstract

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We study a collector's problem with K renewal arrival processes for different type items, where the objective is to collect complete sets. In particular, we derive the asymptotic distribution of the sequence of interarrival times between set completions.

Keywords

Collector's problemcomplete setrenewal processessuperpositionasymptotic distributionmixture

MSC classification

Secondary:60K05: Renewal theory60F05: Central limit and other weak theorems

Information

Type
Research Article
Information
Journal of Applied Probability , Volume 45 , Issue 3 , September 2008, pp. 610 - 620
Copyright
Copyright © Applied Probability Trust 2008 

References

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