Geodesic
Extensions of regularity for a Lévy process
Teoriâ veroâtnostej i ee primeneniâ, Tome 62 (2017) no. 4, pp. 719-752 Cet article a éte moissonné depuis la source Math-Net.Ru

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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. 
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R. A. Maller. Extensions of regularity for a Lévy process. Teoriâ veroâtnostej i ee primeneniâ, Tome 62 (2017) no. 4, pp. 719-752. http://geodesic.mathdoc.fr/item/TVP_2017_62_4_a4/

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