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Asymptotic equivalence of jumps Lévy processes and their discrete counterpart

Pierre Etoré 1 Sana Louhichi 2 Ester Mariucci 2
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 $\{X_t\}$.
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https://hal.archives-ouvertes.fr/hal-00827173
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Submitted on : Thursday, September 19, 2013 - 7:26:55 PM
Last modification on : Saturday, April 30, 2022 - 10:46:01 PM
Long-term archiving on: : Friday, April 7, 2017 - 12:16:31 AM

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

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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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