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Moment estimates for Lévy Processes

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 \cite{MILL} 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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https://hal.archives-ouvertes.fr/hal-00085213
Contributor : Gilles Pagès <>
Submitted on : Wednesday, July 12, 2006 - 10:36:19 AM
Last modification on : Thursday, December 10, 2020 - 12:33:19 PM
Long-term archiving on: : Tuesday, April 6, 2010 - 12:04:23 AM

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Harald Luschgy, Gilles Pagès. Moment estimates for Lévy Processes. Electronic Journal of Probability, Institute of Mathematical Statistics (IMS), 2008, 13, 422-434 : http://dx.doi.org/10.1214/ECP.v13-1397. ⟨10.1214/ECP.v13-1397⟩. ⟨hal-00085213⟩

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