Asymptotic equivalence of jumps Lévy processes and their discrete counterpart

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 $\{X_t\}$.
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Pré-publication, Document de travail
Shorter version focusing on the statistical analysis of the Lévy measure. A new example has been .. 2013
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https://hal.archives-ouvertes.fr/hal-00827173
Contributeur : Ester Mariucci <>
Soumis le : jeudi 19 septembre 2013 - 19:26:55
Dernière modification le : mardi 28 octobre 2014 - 18:33:41
Document(s) archivé(s) le : vendredi 7 avril 2017 - 00:16:31

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

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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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