NONPARAMETRIC ESTIMATION OF SECOND-ORDER STOCHASTIC DIFFERENTIAL EQUATIONS

We propose nonparametric estimators of the infinitesimal coefficients associated with second-order stochastic differential equations+ We show that under appropriate conditions, the proposed estimators are consistent+ Also, we state conditions ensuring the asymptotic normality of these estimators+ We conclude our paper with a Monte Carlo experiment in which we assess the response of the nonparametric estimators with respect to the step of discretization+