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

作者：Mariucci Ester^*

来源：Stochastic Processes and Their Applications, 2016, 126(2): 503-541.

DOI：10.1016/j.spa.2015.09.009

• Nonparametric experiments
• Le Cam distance
• Asymptotic equivalence
• Levy processes

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.

• 出版日期2016-2