Maximum likelihood estimation in Skorohod stochastic differential equations

Abstract

Consistency and limit distribution of the maximum likelihood estimator of a parameter in the drift coefficient of an anticipative Skorohod stochastic differential equation satisfying a boundary condition are obtained based on n n independent trajectories of the corresponding Skorohod diffusion inside a time interval [ 0 , T ] [0, T] as n → ∞ n \rightarrow \infty . The results are illustrated for the anticipative Ornstein-Uhlenbeck process.