Moment estimates for Lévy Processes

Abstract

For real Lévy processes $(X\_t)\_t\ge 0$ 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 $a\_p\in \mathbb{R}$ has been established by Millar \cite{MILL} for $\beta <p\le 2$ provided $X\_1\in L^p$. We derive extensions of these estimates to the cases $p>2$ and $p\le \beta$.

arXiv comment11pages

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