Wat is Markov process, strong Markov property?

An adapted process $(X_t)$ is a Markov process if for all $s, t \ge 0$ and bounded measurable $f$, $\E[f(X_{s+t}) \mid \mathcal F_s] = \E[f(X_{s+t}) \mid X_s]$: given the present, the past adds nothing. It has the strong Markov property if the same holds with $s$ replaced by any finite stopping time $\tau$.