Open Access
August, 1976 A Multidimensional Renewal Theorem
Thomas A. Ryan Jr.
Ann. Probab. 4(4): 656-661 (August, 1976). DOI: 10.1214/aop/1176996034


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.


Published: August, 1976
First available in Project Euclid: 19 April 2007

zbMATH: 0379.60090
MathSciNet: MR418273
Digital Object Identifier: 10.1214/aop/1176996034

Primary: 60K15
Secondary: 60J80 , 60K05

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

Rights: Copyright © 1976 Institute of Mathematical Statistics

Vol.4 • No. 4 • August, 1976
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