# What is a honest Markov process?

I'm having trouble understanding this. Is there a formal definition? –  wircho Apr 24 '12 at 17:54

A Markov process $(X_t)_{t\geqslant0}$ with values in $[0,+\infty]$ is honest if $\mathrm P_x(X(t)=+\infty)=0$ for every time $t$ and every starting point $x$.