Nonparametric inference for discretely sampled Lévy processes

Shota Gugushvili

Annales de l'I.H.P. Probabilités et statistiques (2012)

  • Volume: 48, Issue: 1, page 282-307
  • ISSN: 0246-0203

Abstract

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Given a sample from a discretely observed Lévy process X = (Xt)t≥0 of the finite jump activity, the problem of nonparametric estimation of the Lévy density ρ corresponding to the process X is studied. An estimator of ρ is proposed that is based on a suitable inversion of the Lévy–Khintchine formula and a plug-in device. The main results of the paper deal with upper risk bounds for estimation of ρ over suitable classes of Lévy triplets. The corresponding lower bounds are also discussed.

How to cite

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Gugushvili, Shota. "Nonparametric inference for discretely sampled Lévy processes." Annales de l'I.H.P. Probabilités et statistiques 48.1 (2012): 282-307. <http://eudml.org/doc/271941>.

@article{Gugushvili2012,
abstract = {Given a sample from a discretely observed Lévy process X = (Xt)t≥0 of the finite jump activity, the problem of nonparametric estimation of the Lévy density ρ corresponding to the process X is studied. An estimator of ρ is proposed that is based on a suitable inversion of the Lévy–Khintchine formula and a plug-in device. The main results of the paper deal with upper risk bounds for estimation of ρ over suitable classes of Lévy triplets. The corresponding lower bounds are also discussed.},
author = {Gugushvili, Shota},
journal = {Annales de l'I.H.P. Probabilités et statistiques},
keywords = {empirical characteristic function; empirical process; Fourier inversion; Lévy density; Lévy process; maximal inequality; mean square error},
language = {eng},
number = {1},
pages = {282-307},
publisher = {Gauthier-Villars},
title = {Nonparametric inference for discretely sampled Lévy processes},
url = {http://eudml.org/doc/271941},
volume = {48},
year = {2012},
}

TY - JOUR
AU - Gugushvili, Shota
TI - Nonparametric inference for discretely sampled Lévy processes
JO - Annales de l'I.H.P. Probabilités et statistiques
PY - 2012
PB - Gauthier-Villars
VL - 48
IS - 1
SP - 282
EP - 307
AB - Given a sample from a discretely observed Lévy process X = (Xt)t≥0 of the finite jump activity, the problem of nonparametric estimation of the Lévy density ρ corresponding to the process X is studied. An estimator of ρ is proposed that is based on a suitable inversion of the Lévy–Khintchine formula and a plug-in device. The main results of the paper deal with upper risk bounds for estimation of ρ over suitable classes of Lévy triplets. The corresponding lower bounds are also discussed.
LA - eng
KW - empirical characteristic function; empirical process; Fourier inversion; Lévy density; Lévy process; maximal inequality; mean square error
UR - http://eudml.org/doc/271941
ER -

References

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