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June 1999 Lp estimation of the diffusion coefficient
Marc Hofmann
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Bernoulli 5(3): 447-481 (June 1999).

Abstract

We study the functional estimation of the space-dependent diffusion coefficient in a one-dimensional framework. The sample path is observed at discrete times. We study global L p -loss errors ( 1p<+) over Besov spaces B sp . We show that, under suitable conditions, the minimax rate of convergence is the usual n - s/(1+2s) . Linking our model to nonparametric regression, we provide an estimating procedure based on a linear wavelet method which is optimal in the minimax sense.

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Marc Hofmann. "Lp estimation of the diffusion coefficient." Bernoulli 5 (3) 447 - 481, June 1999.

Information

Published: June 1999
First available in Project Euclid: 27 February 2007

MathSciNet: MR1693608

Keywords: Besov spaces , Diffusion processes , Local time , minimax estimation , Nonparametric regression , wavelet orthonormal bases , wavelets on the internal

Rights: Copyright © 1999 Bernoulli Society for Mathematical Statistics and Probability

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Vol.5 • No. 3 • June 1999
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