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Eigenfunction martingale estimating functions and filtered data for drift estimation of discretely observed multiscale diffusions. (English) Zbl 1484.62001

Summary: We propose a novel method for drift estimation of multiscale diffusion processes when a sequence of discrete observations is given. For the Langevin dynamics in a two-scale potential, our approach relies on the eigenvalues and the eigenfunctions of the homogenized dynamics. Our first estimator is derived from a martingale estimating function of the generator of the homogenized diffusion process. However, the unbiasedness of the estimator depends on the rate with which the observations are sampled. We therefore introduce a second estimator which relies also on filtering the data, and we prove that it is asymptotically unbiased independently of the sampling rate. A series of numerical experiments illustrate the reliability and efficiency of our different estimators.

MSC:

62-08 Computational methods for problems pertaining to statistics
62M05 Markov processes: estimation; hidden Markov models
60H10 Stochastic ordinary differential equations (aspects of stochastic analysis)
60J60 Diffusion processes
62M10 Time series, auto-correlation, regression, etc. in statistics (GARCH)
65C30 Numerical solutions to stochastic differential and integral equations
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