Nonparametric inference for fractional diffusion

Details Nonparametric inference for fractional diffusion Nonparametric inference for fractional diffusion

2011-11-02

arxiv.org/abs/1111.0446v1

Mathematics

Probability

Scientific paper

A non parametric diffusion model with an additive fractional Brownian motion noise is considered in this work. The drift is a non parametric function that will be estimated by two methods. On one hand we propose a locally linear estimator based on the local approximation of the drift by a linear function. On the other hand a Nadaraya-Watson kernel type estimator is studied. In both cases, some non asymptotic results are proposed. An exponential inequality and a kind of law of large numbers for fractional martingales are used to prove the consistency of the Nadaraya-Watson estimator when the Hurst parameter of the driving fractional Brownian motion is less than a half.

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