Estimation for Dynamical Systems with Small Noise from Discrete Observations

Abstract

We consider an efficient estimation of an unknown parameter appearing in both the drift and the diffusion coefficient for a d-dimensional dynamical system with small noise. Asymptotic properties of an M-estimator obtained from an approximate quadratic martingale estimating function are stated. The sample path is observed at equidistant times k/n, k = 0,1,…, n. The type of asymptotics considered is when a small dispersion parameter ε goes to 0 and n goes to ∞ simultaneously.