# Asymptotic equivalence of jumps Lévy processes and their discrete counterpart

1 MATHFI - Mathématiques financières
LJK - Laboratoire Jean Kuntzmann
2 IPS - Inférence Processus Stochastiques
LJK - Laboratoire Jean Kuntzmann
Abstract : We establish the global asymptotic equivalence between a pure jumps Lévy process $\{X_t\}$ on the time interval $[0,T]$ with unknown Lévy measure $\nu$ belonging to a non-parametric class and the observation of $2m^2$ Poisson independent random variables with parameters linked with the Lévy measure $\nu$. The equivalence result is asymptotic as $m$ tends to infinity. The time $T$ is kept fixed and the sample path is continuously observed. This result justifies the idea that, from a statistical point of view, knowing how many jumps fall into a grid of intervals gives asymptotically the same amount of information as observing $\{X_t\}$.
Mots-clés :
Type de document :
Pré-publication, Document de travail
Shorter version focusing on the statistical analysis of the Lévy measure. A new example has been .. 2013
Domaine :

Littérature citée [4 références]

https://hal.archives-ouvertes.fr/hal-00827173
Contributeur : Ester Mariucci <>
Soumis le : jeudi 19 septembre 2013 - 19:26:55
Dernière modification le : lundi 10 décembre 2018 - 15:16:05
Document(s) archivé(s) le : vendredi 7 avril 2017 - 00:16:31

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Mariucci_Preprint.pdf
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• HAL Id : hal-00827173, version 2
• ARXIV : 1305.6725

### Citation

Pierre Etore, Sana Louhichi, Ester Mariucci. Asymptotic equivalence of jumps Lévy processes and their discrete counterpart. Shorter version focusing on the statistical analysis of the Lévy measure. A new example has been .. 2013. 〈hal-00827173v2〉

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