Geodesic
Extensions of regularity for a L\'{e}vy process
Teoriâ veroâtnostej i ee primeneniâ, Tome 62 (2017) no. 4, pp. 719-752

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We obtain necessary and sufficient conditions for the finiteness of certain moment functions of the random variable $T_0^-$, which is the first passage time of a Lévy process $(X_t)_{t\ge 0}$ below zero, and the position $X_{T_0^-}$ of the process at this time. Our results generalize classical results of Rogozin and Bertoin on the regularity of $X$, and extend earlier results of Blumenthal and Getoor on the regularity index.
Keywords: regularity of a real-valued Lévy process, dominance of the positive part of a Lévy process over the negative part, first passage of a Lévy process below zero, first passage time, dominated variation conditions, Rogozin regularity condition. 
@article{TVP_2017_62_4_a4,
     author = {R. A. Maller},
     title = {Extensions of regularity for a {L\'{e}vy} process},
     journal = {Teori\^a vero\^atnostej i ee primeneni\^a},
     pages = {719--752},
     publisher = {mathdoc},
     volume = {62},
     number = {4},
     year = {2017},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TVP_2017_62_4_a4/}
}
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R. A. Maller. Extensions of regularity for a L\'{e}vy process. Teoriâ veroâtnostej i ee primeneniâ, Tome 62 (2017) no. 4, pp. 719-752. http://geodesic.mathdoc.fr/item/TVP_2017_62_4_a4/