View source for Ray-Knight compactification

A powerful tool to study homogeneous [[Markov_process#The_strong_Markov_property.|strong Markov processes]] under some general hypotheses. The idea is to imbed as a set the state space $E$ of the process in a compact metrizable space $\hat E$ such that the [[resolvent]] $(U_p)_{p\ge 0}$ of the [[transition-operator semi-group]] $(P_t)_{t\ge0}$> has a unique extension to $\hat E$ as a resolvent $(\hat U_p)$ with nice analytical properties. This Ray resolvent is associated to a semi-group $(\hat P_t)$ (note that $\hat P_0$ need not be the identity: existence of branching points), quite indistinguishable from $(P_t)$ on $E$. The Ray–Knight compactification allows one to extend easily numerous important results for [[Feller process]]es to strong Markov processes, to define entrance boundaries, etc.

====References====
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<TR><TD valign="top">[a1]</TD> <TD valign="top">  C. Dellacherie,   P.A. Meyer,   "Probabilities and potential" , '''C''' , North-Holland  (1988)  pp. Chapt. XII  (Translated from French)</TD></TR>
<TR><TD valign="top">[a2]</TD> <TD valign="top">  R.K. Getoor,   "Markov processes: Ray processes and right processes" , ''Lect. notes in math.'' , '''440''' , Springer  (1975)</TD></TR>
<TR><TD valign="top">[a3]</TD> <TD valign="top">  M.J. Sharpe,   "General theory of Markov processes" , Acad. Press  (1988)</TD></TR>
</table>

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