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.I thank two anonymous referees who made valuable suggestions that led to considerable improvements in the paper. I am also grateful to Carlos Braumann and Tom Kundert for helpful comments. This research was supported by the Fundação para a Ciência e a Tecnologia (FCT) and by FEDER/POCI 2010.