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October, 1981 Regular Birth Times for Markov Processes
A. O. Pittenger
Ann. Probab. 9(5): 769-780 (October, 1981). DOI: 10.1214/aop/1176994307

Abstract

A random time $R$ is called a regular birth time for a Markov Process if (i) the $R$-past and $R$-future are conditionally independent with respect to $X(R)$ and (ii) the post-$R$ process evolves as a Markov process, perhaps with different probability laws. In this paper we characterize each regular birth time in terms of an earlier, coterminal time $L$. It is shown (Theorem 4.2) that to the post-$L$ process $R$ appears as an optional time, perhaps with dependency on pre-$L$ information and on a certain invariant set.

Citation

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A. O. Pittenger. "Regular Birth Times for Markov Processes." Ann. Probab. 9 (5) 769 - 780, October, 1981. https://doi.org/10.1214/aop/1176994307

Information

Published: October, 1981
First available in Project Euclid: 19 April 2007

zbMATH: 0475.60055
MathSciNet: MR628872
Digital Object Identifier: 10.1214/aop/1176994307

Subjects:
Primary: 60J25
Secondary: 60G40

Keywords: coterminal times , regular birth times , strong Markov processes , strong Markov property

Rights: Copyright © 1981 Institute of Mathematical Statistics

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Vol.9 • No. 5 • October, 1981
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