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Renewal theory for embedded regenerative sets


Bertoin, Jean (2000). Renewal theory for embedded regenerative sets. The Annals of Probability, 27(3):1523-1535.

Abstract

We consider the age processes A(1)≥⋯≥A(n) associated to a monotone sequence R(1)⊆⋯⊆R(n) of regenerative sets. We obtain limit theorems in distribution for (A_t^{(1)},\ldots, A_t^{(n)})andfor((1/t) A_t^{(1)},\ldots,(1/t)A_t^{(n)})$, which correspond to multivariate versions of the renewal theorem and of the Dynkin–Lamperti theorem, respectively. Dirichlet distributions play a key role in the latter.

Abstract

We consider the age processes A(1)≥⋯≥A(n) associated to a monotone sequence R(1)⊆⋯⊆R(n) of regenerative sets. We obtain limit theorems in distribution for (A_t^{(1)},\ldots, A_t^{(n)})andfor((1/t) A_t^{(1)},\ldots,(1/t)A_t^{(n)})$, which correspond to multivariate versions of the renewal theorem and of the Dynkin–Lamperti theorem, respectively. Dirichlet distributions play a key role in the latter.

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Additional indexing

Item Type:Journal Article, refereed, original work
Communities & Collections:07 Faculty of Science > Institute of Mathematics
Dewey Decimal Classification:510 Mathematics
Language:English
Date:2000
Deposited On:25 Jul 2013 06:39
Last Modified:05 Apr 2016 16:52
Publisher:Institute of Mathematical Statistics
ISSN:0091-1798
Free access at:Publisher DOI. An embargo period may apply.
Publisher DOI:https://doi.org/10.1214/aop/1022677457
Related URLs:http://www.ams.org/mathscinet-getitem?mr=1733158
http://www.zentralblatt-math.org/zbmath/search/?q=an%3A0961.60082

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