Hi, 


probably this is a fairly newbie question, but is it possible that the a generic Levy process explodes (i.e. tends to infinity for finite time t with positive probability)? If yes, could you please provide an example, if no point me to the proof.



Exploding Levy processes
Hi,


As remarked by Leonid Kovalev a Lévy process doesn't explodes as far as I know, nevertheless as you mention generic Levy Process for which I don't know any definition, you may be thinking of them as diffusions driven by a Lévy process. 


Then looking at some SDEs, you can have some cases where explosion time is a.s. finite, and even when the driving procsess is a Brownian Motion, for example I think I can remember that $X\_t$ verifying $d[Ln(X\_t)]=a(b-Ln(X\_t))dt+\sigma.dW\_t$, $X\_0=0$ is of this type.


(for references, google at "Black-Karasinski short rate model")


Regards


