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April, 1978 A Path Decomposition for Markov Processes
P. W. Millar
Ann. Probab. 6(2): 345-348 (April, 1978). DOI: 10.1214/aop/1176995581

Abstract

Let $X = \{X_t, t > 0\}$ be a right continuous strong Markov process with state space $E$; let $f$ be a continuous real valued function on $E \times E$; and let $M$ be the time at which the process $\{f(X_{t-}, X_t)\}$ achieves its (last) ultimate minimum. Then conditional on $X_M$ and the value of this minimum, the process $\{X_{M + t}\}$ is Markov and (conditionally) independent of events before $M$.

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P. W. Millar. "A Path Decomposition for Markov Processes." Ann. Probab. 6 (2) 345 - 348, April, 1978. https://doi.org/10.1214/aop/1176995581

Information

Published: April, 1978
First available in Project Euclid: 19 April 2007

zbMATH: 0379.60070
MathSciNet: MR461678
Digital Object Identifier: 10.1214/aop/1176995581

Subjects:
Primary: 60J25
Secondary: 60G40 , 60J40

Keywords: generalized strong Markov property , last exit decomposition , Markov process , minimum , Path decomposition

Rights: Copyright © 1978 Institute of Mathematical Statistics

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Vol.6 • No. 2 • April, 1978
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