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Moment estimates for Lévy Processes

   
@article{ECP1397,
	author = {Harald Luschgy and Gilles Pagès},
	title = {Moment estimates for Lévy Processes},
	journal = {Electron. Commun. Probab.},
	fjournal = {Electronic Communications in Probability},
	volume = {13},
	year = {2008},
	keywords = {Levy process increment; Levy measure; alpha-stable process; Normal Inverse Gaussian process; tempered stable process; Meixner process.},
	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 $p \leq\beta$.},
	pages = {no. 41, 422-434},
	issn = {1083-589X},
	doi = {10.1214/ECP.v13-1397},    
        url = {http://ecp.ejpecp.org/article/view/1397}}