Parametric inference for multidimensional hypoelliptic diffusion with full observations.

Multidimensional hypoelliptic diffusions arise naturally as models ofneuronal activity. Estimation in those models is complex because of thedegenerate structure of the diffusion coefficient. We build a consistentestimator of the drift and variance parameters with the help of a discretizedlog-likelihood of the continuous process in the case of fully observed data. Wediscuss the difficulties generated by the hypoellipticity and provide a proofof the consistency of the estimator. We test our approach numerically on thehypoelliptic FitzHugh-Nagumo model, which describes the firing mechanism of aneuron.