The Annals of Probability

Birth, Death and Conditioning of Markov Chains

M. Jacobsen and J. W. Pitman

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Abstract

Given a Markov chain with stationary transition probabilities, we study random times $\tau$ determined by the evolution of the Markov chain for which either the pre-$\tau$ or post-$\tau$ process is Markovian with stationary transition probabilities. A complete description is given of all such random times which admit a conditional independence property analogous to the strong Markov property at a stopping time.

Article information

Source
Ann. Probab., Volume 5, Number 3 (1977), 430-450.

Dates
First available in Project Euclid: 19 April 2007

Permanent link to this document
https://projecteuclid.org/euclid.aop/1176995803

Digital Object Identifier
doi:10.1214/aop/1176995803

Mathematical Reviews number (MathSciNet)
MR445613

Zentralblatt MATH identifier
0363.60052

JSTOR
links.jstor.org

Subjects
Primary: 60J10: Markov chains (discrete-time Markov processes on discrete state spaces)
Secondary: 60G40: Stopping times; optimal stopping problems; gambling theory [See also 62L15, 91A60]

Keywords
Markov chain path decomposition birth time death time conditional independence of path fragments

Citation

Jacobsen, M.; Pitman, J. W. Birth, Death and Conditioning of Markov Chains. Ann. Probab. 5 (1977), no. 3, 430--450. doi:10.1214/aop/1176995803. https://projecteuclid.org/euclid.aop/1176995803


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