Asymptotic equivalence for diffusion processes and the corresponding Euler scheme

Ester Mariucci, Universität Potsdam, SFB 1294, Germany - 11:15

When looking for asymptotic results for some statistical model, global asymptotic equivalence, in the Le Cam sense, often proves to be a useful tool that allows 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 diffusion processes. More precisely, I will present a global asymptotic equivalence result, in the sense of the Le Cam $\Delta$-distance, between scalar diffusion models with unknown drift function and small variance on the one side, and the corresponding Euler scheme on the other side. The time horizon T is
kept fixed and both the cases of discrete and continuous observation of the path are treated. The diffusion coefficient is non-constant, bounded but possibly tending to zero. The asymptotic equivalences are established by constructing explicit equivalence mappings.


Ester Mariucci is currently a deputy professor at the Institute of Mathematics at the University of Potsdam.