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Estimating equations based on eigenfunctions for a discretely observed diffusion process. (English) Zbl 0980.62074
Summary: A new type of martingale estimating functions is proposed for inference about classes of diffusion processes based on discrete-time observations. These estimating functions can be tailored to a particular class of diffusion processes by utilizing a martingale property of the eigenfunctions of the generators of the diffusions.
Optimal estimating functions in the sense of V.P. Godambe and C.C. Heyde [Int. Stat. Rev. 55, 231-244 (1987; Zbl 0671.62007)] are found. Inference based on these is invariant under transformations of data. A result on consistency and asymptotic normality of the estimators is given for ergodic diffusions. The theory is illustrated by several examples and by a simulation study.

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