Asymptotic equivalence for time continuous additive processes and their discrete counterpart

Pierre Etoré (1) , Sana Louhichi (1) , Ester Mariucci (1)

1 LJK - Laboratoire Jean Kuntzmann

We establish the global asymptotic equivalence between a pure jumps Lévy process with unknown Lévy measure $\nu$ and a sequence of independent Poisson random variables with parameters depending on $\nu$. Combining this result with the one in Brown and Low (1996), we deduce an asymptotic equivalence between an additive process with unknown drift and Lévy measure and a discrete model composed by a non-parametric regression plus some independent Poisson random variables.

Mots clés: non-parametric regression; Non-parametric experiments; deficiency distance; asymptotic equivalence; Lévy processes; additive processes; non-parametric regression.

Domaines: Probabilités [math.PR]; Statistiques [math.ST]; Théorie [stat.TH]

Pierre Etoré, Sana Louhichi, Ester Mariucci. Asymptotic equivalence for time continuous additive processes and their discrete counterpart. 2013. ⟨hal-00827173v1⟩