Open Access
2015 Limits of renewal processes and Pitman-Yor distribution
Bojan Basrak
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Electron. Commun. Probab. 20: 1-13 (2015). DOI: 10.1214/ECP.v20-4080


We consider a renewal process with regularly varying stationary and weakly dependent steps, and prove that the steps made before a given time $t$, satisfy an interesting invariance principle. Namely, together with the age of the renewal process at time $t$, they converge after scaling to the Pitman–Yor distribution. We further discuss how our results extend the classical Dynkin–Lamperti theorem.


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Bojan Basrak. "Limits of renewal processes and Pitman-Yor distribution." Electron. Commun. Probab. 20 1 - 13, 2015.


Accepted: 18 July 2015; Published: 2015
First available in Project Euclid: 7 June 2016

zbMATH: 1327.60080
MathSciNet: MR3374301
Digital Object Identifier: 10.1214/ECP.v20-4080

Primary: 60F17
Secondary: 60F05 , 60G55 , 60G70

Keywords: Dynkin–Lamperti theorem , invariance principle , Pitman–Yor distribution , point process , regular variation , Renewal process

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