Asymptotic equivalence of jumps Lévy processes and their discrete counterpart

2013/05/29 by Pierre Étoré, Étoré, Pierre, Sana Louhichi +3
Mathematics · #FOS: Mathematics #Probability (math.PR) #math.PR

paper · pdf · doi:10.48550/arxiv.1305.6725

Shorter version focusing on the statistical analysis of the Lévy measure. A new example has been added

arxiv created 2013/09/19 · arxiv updated 2013/09/20

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 ν belonging to a non-parametric class and the observation of 2m² Poisson independent random variables with parameters linked with the Lévy measure ν. 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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