• Bernoulli
  • Volume 20, Number 2 (2014), 878-918.

Nonparametric inference for fractional diffusion

Bruno Saussereau

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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 by means of deviation probability bound. The consistency property of the estimators are obtained under a one sided dissipative Lipschitz condition on the drift that insures the ergodic property for the stochastic differential equation. Our estimators are first constructed under continuous observations. The drift function is then estimated with discrete time observations that is of the most importance for practical applications.

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Bernoulli, Volume 20, Number 2 (2014), 878-918.

First available in Project Euclid: 28 February 2014

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fractional Brownian motion non-parametric fractional diffusion model statistical inference stochastic differential equation


Saussereau, Bruno. Nonparametric inference for fractional diffusion. Bernoulli 20 (2014), no. 2, 878--918. doi:10.3150/13-BEJ509.

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