Asymptotic equivalence of diffusion processes and its Euler scheme: small variance case
jeudi 12 mars 2015, 13h30 - 14h30
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 diffusion models. More precisely, I will discuss the global asymptotic equivalence between scalar diffusion models with unknown drift function and small variance on the one side, and nonparametric autoregressive models 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 asymptotic equivalences are established by constructing explicit Markov kernels that can be used to reproduce one experiment from the other.