Asymptotic equivalence for pure jump Lévy processes with unknown Lévy density and Gaussian white noise
Abstract
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 L{é}vy process and a Gaussian white noise experiment observed up to a time T, with T tending to $\infty$. These approximations are given in the sense of the Le Cam distance, under some smoothness conditions on the unknown L{é}vy density. All the asymptotic equivalences are established by constructing explicit Markov kernels that can be used to reproduce one experiment from the other.
 Publication:

arXiv eprints
 Pub Date:
 March 2015
 arXiv:
 arXiv:1503.04530
 Bibcode:
 2015arXiv150304530M
 Keywords:

 Mathematics  Probability;
 Mathematics  Statistics Theory
 EPrint:
 50 pages. The definition of the parameter space has changed and some proofs have been expanded and corrected