A Multidimensional Renewal Theorem

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August, 1976 A Multidimensional Renewal Theorem

Thomas A. Ryan Jr.

Ann. Probab. 4(4): 656-661 (August, 1976). DOI: 10.1214/aop/1176996034

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Abstract

A multidimensional renewal theorem is proven which generalizes the well-known result of Pyke on Markov renewal processes. The result is a "natural" setting of the multidimensional renewal theorem, and has applications to age-dependent branching processes.

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Thomas A. Ryan Jr.. "A Multidimensional Renewal Theorem." Ann. Probab. 4 (4) 656 - 661, August, 1976. https://doi.org/10.1214/aop/1176996034

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Published: August, 1976

First available in Project Euclid: 19 April 2007

zbMATH: 0379.60090

MathSciNet: MR418273

Digital Object Identifier: 10.1214/aop/1176996034

Subjects:

Primary: 60K15

Secondary: 60J80 , 60K05

Keywords: age-dependent branching process , Markov renewal process , Multidimensional renewal theorem

Rights: Copyright © 1976 Institute of Mathematical Statistics

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Ann. Probab.

Vol.4 • No. 4 • August, 1976

Institute of Mathematical Statistics

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Thomas A. Ryan Jr. "A Multidimensional Renewal Theorem," The Annals of Probability, Ann. Probab. 4(4), 656-661, (August, 1976)

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