Asymptotic equivalence for inhomogeneous jump diffusion processes and white noise

Laboratoire Jean Kuntzmann, 51 rue des Mathématiques, 38041 Grenoble cedex 09, France.
ester.mariucci@imag.fr

Received: 3 May 2014
Revised: 4 February 2015

Abstract

We prove the global asymptotic equivalence between the experiments generated by the discrete (high frequency) or continuous observation of a path of a time inhomogeneous jump-diffusion process and a Gaussian white noise experiment. Here, the parameter of interest is the drift function and the observation time T can be both bounded or diverging. The approximation is given in the sense of the Le Cam Δ-distance, under some smoothness conditions on the unknown drift function. These asymptotic equivalences are established by constructing explicit Markov kernels that can be used to reproduce one experiment from the other.