Can anyone give an example of a Markov process which is not a strong Markov process? The Markov property and strong Markov property are typically introduced as distinct concepts (for example in Oksendal's book on stochastic analysis), but I've never seen a process which satisfies one but not the other.


Many thanks
-Simon



A Markov process which is not a strong markov process?
Consider the following continuous Markov process X, starting from position x


1. if x = 0 then Xt = 0 for all times.
2. if x ≠ 0 then X is a standard Brownian motion starting from x.


This is not strong Markov (look at times at which it hits zero).


