Résumé : Multidimensional hypoelliptic diffusions arise naturally as models
of neuronal activity. Estimation in those models is complex because of
the degenerate structure of the diffusion coefficient. We build a consis-
tent estimator of the drift and variance parameters with the help of a
discretized log-likelihood of the continuous process in the case of fully
observed data. We discuss the difficulties generated by the hypoel-
lipticity and provide a proof of the consistency of the estimator. We
test our approach numerically on the hypoelliptic FitzHugh-Nagumo
model, which describes the firing mechanism of a neuron.