I have a question as follow:
"Let $X$ be a general Markov process, $M$ is a running maximum process of $X$ and $T$ be an exponential distribution, independent of $X$.
I learned that there is the following result:
Probability: $P_x(X_T\in dz \mid M_T=y)$ is independent of starting point $x$ of the process $X$. Where $y, z \in R$"
Is there anyone who knows some references which mentioned the result above? I heard that this result was found around the seventies but I haven't found any good reference yet.
Thanks a lot!