Moment estimates for Lévy Processes
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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Pages: 422-434
Publication Date: August 5, 2008
DOI: 10.1214/ECP.v13-1397
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