A Path Decomposition for Markov Processes
Millar, P. W.
Ann. Probab., Tome 6 (1978) no. 6, p. 345-348 / Harvested from Project Euclid
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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 $M$.
Publié le : 1978-04-14
Classification:  Markov process,  generalized strong Markov property,  path decomposition,  minimum,  last exit decomposition,  60J25,  60J40,  60G40 
@article{1176995581,
     author = {Millar, P. W.},
     title = {A Path Decomposition for Markov Processes},
     journal = {Ann. Probab.},
     volume = {6},
     number = {6},
     year = {1978},
     pages = { 345-348},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1176995581}
}

Millar, P. W. A Path Decomposition for Markov Processes. Ann. Probab., Tome 6 (1978) no. 6, pp.  345-348. http://gdmltest.u-ga.fr/item/1176995581/