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Nonparametric estimation of the diffusion coefficient of a diffusion process. (English) Zbl 0894.62093

Summary: This paper deals with the nonparametric estimation of the diffusion coefficient of a diffusion process in the case when it depends only on time. The estimator is based on the regularization of the quadratic mean through multiscale analysis. We then define estimators of the second derivative of the diffusion coefficient, in order to obtain optimal bandwidth and to perform a test of linearity. The results we obtain are quite similar to those of the estimation of the density function of an i.i.d. sequence.

MSC:

62M02 Markov processes: hypothesis testing
62G05 Nonparametric estimation
62G20 Asymptotic properties of nonparametric inference
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References:

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