Asymptotic equivalence of jumps Lévy processes and their discrete counterpart - Archive ouverte HAL
Pré-Publication, Document De Travail Année : 2013

Asymptotic equivalence of jumps Lévy processes and their discrete counterpart

Pierre Etoré
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Sana Louhichi
Ester Mariucci
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Résumé

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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Dates et versions

hal-00827173 , version 1 (29-05-2013)
hal-00827173 , version 2 (19-09-2013)

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Pierre Etoré, Sana Louhichi, Ester Mariucci. Asymptotic equivalence of jumps Lévy processes and their discrete counterpart. 2013. ⟨hal-00827173v2⟩
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