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Jun 16, 2018 at 9:58 comment added Mateusz Kwaśnicki For stable processes $S_t$ (at least in continuous time), I suppose self-similarity helps: $Z_t = t^{-1/p} S_t$ is a self-similar Markov process, and the question is whether it stays away from zero or not. This seems to be a well-studied problem. Kyprianou's three papers on "Deep factorisation of the stable process" seem to be a good entry point into related literature.
May 1, 2018 at 14:14 comment added Goulifet lim inf! The lim sup is treated in the paper of Pruitt (as an easy consequence of the study with $M_N$).
May 1, 2018 at 13:50 comment added Mikael de la Salle $\liminf$ or $\limsup$?
May 1, 2018 at 9:48 history asked Goulifet CC BY-SA 3.0