We investigate the connections between the mean pathwise regularity of stochastic processes and their Lr(ℙ)-functional quantization rates as random variables taking values in some Lp([0, T], dt)-spaces (0−1/2) upper bound for general Itô processes which include multidimensional diffusions. Then, we focus on the specific family of Lévy processes for which we derive a general quantization rate based on the regular variation properties of its Lévy measure at 0. The case of compound Poisson processes, which appear as degenerate in the former approach, is studied specifically: we observe some rates which are between the finite-dimensional and infinite-dimensional “usual” rates.
Publié le : 2008-04-15
Classification:
Functional quantization,
Gaussian process,
Haar basis,
Lévy process,
Poisson process,
60E99,
60G51,
60G15,
60G52,
60J60
@article{1206018193,
author = {Luschgy, Harald and Pag\`es, Gilles},
title = {Functional quantization rate and mean regularity of processes with an application to L\'evy processes},
journal = {Ann. Appl. Probab.},
volume = {18},
number = {1},
year = {2008},
pages = { 427-469},
language = {en},
url = {http://dml.mathdoc.fr/item/1206018193}
}
Luschgy, Harald; Pagès, Gilles. Functional quantization rate and mean regularity of processes with an application to Lévy processes. Ann. Appl. Probab., Tome 18 (2008) no. 1, pp. 427-469. http://gdmltest.u-ga.fr/item/1206018193/