Asymptotic equivalence for pure jump Levy processes with unknown Levy density and Gaussian white noise

STOCHASTIC PROCESSES AND THEIR APPLICATIONS

卷:126

Article

Mariucci, Ester¹ 

[1] Univ Grenoble 1, Lab LJK, UMR 5224, 51,Rue Math,St Martin dHeres BP 53, F-38041 Grenoble 09, France

关键词: Nonparametric experiments;    Le Cam distance;    Asymptotic equivalence;    Levy processes;   

DOI  :  10.1016/j.spa.2015.09.009

来源: Elsevier

【 摘 要 】

The aim of this paper is to establish a global asymptotic equivalence between the experiments generated by the discrete (high frequency) or continuous observation of a path of a Levy process and a Gaussian white noise experiment observed up to a time T, with T tending to infinity. These approximations are given in the sense of the Le Cam distance, under some smoothness conditions on the unknown Levy density. All the asymptotic equivalences are established by constructing explicit Markov kernels that can be used to reproduce one experiment from the other. (C) 2015 Elsevier B.V. All rights reserved.

【 授权许可】

Free