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August, 1984 Two Operational Characterizations of Cooptional Times
Martin Jacobsen
Ann. Probab. 12(3): 714-725 (August, 1984). DOI: 10.1214/aop/1176993222


Consider a random time $\tau$ determined by the evolution of a Markov chain $X$ in discrete time and with discrete state space. Assuming that the pre-$\tau$ and post-$\tau$ processes are conditionally independent given $X_{\tau-1}$ and $0 < \tau < \infty$, it is shown that: (i) the pre-$\tau$ process reversed is Markov and in natural duality to $X$ if and only if $\tau$ is almost surely equal to a modified cooptional time; (ii) the pre-$\tau$ process itself is Markov and an $h$-transform of $X$ if and only if $\tau$ is almost surely equal to a cooptional time with, in general, the possible starts for the pre-$\tau$ process restricted. Also, a result is presented characterizing those $\tau$ for which the reversed pre-$\tau$ process is Markov in natural duality to $X$, without the assumption of conditional independence.


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Martin Jacobsen. "Two Operational Characterizations of Cooptional Times." Ann. Probab. 12 (3) 714 - 725, August, 1984.


Published: August, 1984
First available in Project Euclid: 19 April 2007

zbMATH: 0546.60067
MathSciNet: MR744228
Digital Object Identifier: 10.1214/aop/1176993222

Primary: 60J10
Secondary: 60J35

Keywords: $h$-transforms , cooptional times , Death times

Rights: Copyright © 1984 Institute of Mathematical Statistics

Vol.12 • No. 3 • August, 1984
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