Section: New Results

Non-parametric estimation for kinetic diffusions

Participant : Clémentine Prieur.

This research is the subject of a collaboration with Venezuela (Professor Jose R. Leon, Caracas Central University) and is partly funded by an ECOS Nord project.

We are focusing our attention on models derived from the linear Fokker-Planck equation. From a probabilistic viewpoint, these models have received particular attention in recent years, since they are a basic example for hypercoercivity. In fact, even though completely degenerated, these models are hypoelliptic and still verify some properties of coercivitiy, in a broad sense of the word. Such models often appear in the fields of mechanics, finance and even biology. For such models we believe it appropriate to build statistical non-parametric estimation tools. Initial results have been obtained for the estimation of invariant density, in conditions guaranteeing its existence and unicity [8] and when only partial observational data are available. A paper on the non parametric estimation of the drift has been submitted recently [62] (see Samson et al., 2012, for results for parametric models). As far as the estimation of the diffusion term is concerned, we obtained promising results, in collaboration with J.R. León (Caracas, Venezuela) and P. Cattiaux (Toulouse). These results should be submitted shortly.