%0 Journal Article %1 1978 %A Millar, P. W. %D 1978 %I Institute of Mathematical Statistics %J The Annals of Probability %K Markov_processes path_decomposition %N 2 %P 345--348 %T A Path Decomposition for Markov Processes %U http://www.jstor.org/stable/2243226 %V 6 %X 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 $E E$; 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{1978, 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 $M$.}, added-at = {2009-11-19T05:23:41.000+0100}, author = {Millar, P. W.}, biburl = {https://www.bibsonomy.org/bibtex/208fe9aeb5dcb40df40ca141a89921d89/peter.ralph}, copyright = {Copyright © 1978 Institute of Mathematical Statistics}, interhash = {c36eebdf922c4614c62fd03934d843a6}, intrahash = {08fe9aeb5dcb40df40ca141a89921d89}, issn = {00911798}, journal = {The Annals of Probability}, jstor_articletype = {primary_article}, jstor_formatteddate = {Apr., 1978}, keywords = {Markov_processes path_decomposition}, number = 2, pages = {345--348}, publisher = {Institute of Mathematical Statistics}, timestamp = {2009-11-19T05:23:41.000+0100}, title = {A Path Decomposition for Markov Processes}, url = {http://www.jstor.org/stable/2243226}, volume = 6, year = 1978 }