Approximate martingale estimating functions for stochastic differential equations with small noises |
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Authors: | Masayuki Uchida |
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Affiliation: | Graduate School of Engineering Science, Osaka University, 1-3 Machikaneyama-chou Toyonaka 560-8531, Japan |
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Abstract: | 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 ε from discrete time observations at n regularly spaced time points k/n, k=0,1,…,n. We show asymptotic efficiency of an M-estimator derived from the approximate martingale estimating function as ε→0 and n→∞ simultaneously. |
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Keywords: | primary, 62F12, 62M05 secondary, 60J60 |
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