Moment estimates for Lévy Processes
Harald Luschgy, Univ. Trier
Gilles Pagès, Univ. Paris 6
Abstract
For real Lévy processes $(X_t)_{t geq 0}$ having no Brownian component with Blumenthal-Getoor index $beta$, the estimate $E sup_{s leq t} |X_s - a_p s|^p leq C_p t$ for every $t in [0,1]$ and suitable $a_p in R$ has been established by Millar for $beta < p leq 2$ provided $X_1 in L^p$. We derive extensions of these estimates to the cases $p > 2$ and $p leq beta$.
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