The Annals of Probability

A Path Decomposition for Markov Processes

P. W. Millar

Full-text: Open access

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 $M$.

Article information

Source
Ann. Probab., Volume 6, Number 2 (1978), 345-348.

Dates
First available in Project Euclid: 19 April 2007

Permanent link to this document
https://projecteuclid.org/euclid.aop/1176995581

Digital Object Identifier
doi:10.1214/aop/1176995581

Mathematical Reviews number (MathSciNet)
MR461678

Zentralblatt MATH identifier
0379.60070

JSTOR
links.jstor.org

Subjects
Primary: 60J25: Continuous-time Markov processes on general state spaces
Secondary: 60J40: Right processes 60G40: Stopping times; optimal stopping problems; gambling theory [See also 62L15, 91A60]

Keywords
Markov process generalized strong Markov property path decomposition minimum last exit decomposition

Citation

Millar, P. W. A Path Decomposition for Markov Processes. Ann. Probab. 6 (1978), no. 2, 345--348. doi:10.1214/aop/1176995581. https://projecteuclid.org/euclid.aop/1176995581


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