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I'm having trouble understanding this. Is there a formal definition? – wircho Apr 24 '12 at 17:54
up vote 3 down vote accepted

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 $x$.

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