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June, 1979 Infinite Divisibility in Stochastic Processes
H. D. Miller
Ann. Probab. 7(3): 406-417 (June, 1979). DOI: 10.1214/aop/1176995042

Abstract

It is shown that infinite divisibility of random variables, such as first passage times in a stochastic process, is often connected with the existence of an imbedded terminating renewal process. The idea is used to prove that for a continuous time Markov chain with two, three or four states all first passage times are infinitely divisible but for more than four states there are first passage times which are not infinitely divisible.

Citation

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H. D. Miller. "Infinite Divisibility in Stochastic Processes." Ann. Probab. 7 (3) 406 - 417, June, 1979. https://doi.org/10.1214/aop/1176995042

Information

Published: June, 1979
First available in Project Euclid: 19 April 2007

zbMATH: 0401.60014
MathSciNet: MR528319
Digital Object Identifier: 10.1214/aop/1176995042

Subjects:
Primary: 60E05
Secondary: 60J10, 60K05

Rights: Copyright © 1979 Institute of Mathematical Statistics

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Vol.7 • No. 3 • June, 1979
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