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I read this term in: http://www.proba.jussieu.fr/pageperso/amaury/index_fichiers/Guanajuato.pdf

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    I'm having trouble understanding this. Is there a formal definition?2012-04-24

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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 $x$.