01.02.2023, 14:15 Uhr
– Raum 2.09.2.22 und Zoom, Public Viewing im Raum 2.09.0.17
Dr. Siegfried Beckus (UP)
Ester Mariucci (Universität Potsdam)
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 Δ-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.