Adaptive estimation in diffusion processes. (English) Zbl 1043.62528

Summary: We study the nonparametric estimation of the coefficients of a 1-dimensional diffusion process from discrete observations. Different asymptotic frameworks are considered. Minimax rates of convergence are studied over a wide range of Besov smoothness classes. We construct estimators based on wavelet thresholding which are adaptive (with respect to an unknown degree of smoothness). The results are comparable with simpler models such as density estimation or nonparametric regression.


62M05 Markov processes: estimation; hidden Markov models
62G05 Nonparametric estimation
62G20 Asymptotic properties of nonparametric inference
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