Approximate martingale estimating functions for stochastic differential equations with small noises. (English) Zbl 1145.62065

Summary: An approximate martingale estimating function with an eigenfunction is proposed for an estimation problem about an unknown drift parameter for a one-dimensional diffusion process with small perturbed parameter \(\epsilon \) from discrete time observations at \(n\) regularly spaced time points \(k/n, k=0,1,\cdots ,n\). We show the asymptotic efficiency of an \(M\)-estimator derived from the approximate martingale estimating function as \(\varepsilon \rightarrow 0\) and \(n\rightarrow \infty \) simultaneously.


62M05 Markov processes: estimation; hidden Markov models
62F12 Asymptotic properties of parametric estimators
60H10 Stochastic ordinary differential equations (aspects of stochastic analysis)
60J60 Diffusion processes
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