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December, 1964 Limit Theorems for Markov Renewal Processes
Ronald Pyke, Ronald Schaufele
Ann. Math. Statist. 35(4): 1746-1764 (December, 1964). DOI: 10.1214/aoms/1177700397

Abstract

This paper is a study of Doeblin Ratio limit laws, the weak and strong laws of large numbers, and the Central Limit theorem for Markov Renewal processes. A general definition of these processes is given in Section 2. The means and variances of random variables associated with recurrence times are computed in Section 4. When restricted to the special case of a Markov chain, certain of the results of Sections 5 and 6 strengthen known results.

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Ronald Pyke. Ronald Schaufele. "Limit Theorems for Markov Renewal Processes." Ann. Math. Statist. 35 (4) 1746 - 1764, December, 1964. https://doi.org/10.1214/aoms/1177700397

Information

Published: December, 1964
First available in Project Euclid: 27 April 2007

zbMATH: 0134.34602
MathSciNet: MR168026
Digital Object Identifier: 10.1214/aoms/1177700397

Rights: Copyright © 1964 Institute of Mathematical Statistics

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Vol.35 • No. 4 • December, 1964
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