Bernoulli

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

Nonparametric inference for fractional diffusion

Bruno Saussereau

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Abstract

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.

Article information

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

Dates
First available in Project Euclid: 28 February 2014

Permanent link to this document
https://projecteuclid.org/euclid.bj/1393594009

Digital Object Identifier
doi:10.3150/13-BEJ509

Mathematical Reviews number (MathSciNet)
MR3178521

Zentralblatt MATH identifier
06291825

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

Citation

Saussereau, Bruno. Nonparametric inference for fractional diffusion. Bernoulli 20 (2014), no. 2, 878--918. doi:10.3150/13-BEJ509. https://projecteuclid.org/euclid.bj/1393594009


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