Asymptotic equivalence for discretely or continously observed Lévy processes and Gaussian white noise

Ester Mariucci (Grenoble)
Wednesday, November 12, 2014 - 10:00am
WIAS, Erhard-Schmidt-Saal, Mohrenstraße 39, 10117 Berlin

When looking for asymptotic results for some statistical model it is often useful to dispose of a global asymptotic equivalence, in the Le Cam sense, in order to be allowed to work in a simpler model. In this talk, after giving an introduction to the main characters involved in the Le Cam theory, I will focus on equivalence results for Lévy processes. I will discuss global asymptotic equivalences between the experiments generated by the discrete (high frequency) or continuous observation of a path of a Lévy process and a Gaussian white noise experiment. I will first focus on the case in which the considered parameter is the drift function; then the setting will be extended to include the Lévy density as an unknown parameter. These approximations are given in the sense of the Le Cam $\Delta$-distance, under smoothness conditions on the unknown drift function and Lévy density. All the asymptotic equivalences are established by constructing explicit Markov kernels that can be used to reproduce one experiment from the other.