Bernoulli

  • Bernoulli
  • Volume 5, Number 3 (1999), 447-481.

Lp estimation of the diffusion coefficient

Marc Hofmann

Full-text: Open access

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.

Article information

Source
Bernoulli, Volume 5, Number 3 (1999), 447-481.

Dates
First available in Project Euclid: 27 February 2007

Permanent link to this document
https://projecteuclid.org/euclid.bj/1172617199

Mathematical Reviews number (MathSciNet)
MR1693608

Keywords
Besov spaces diffusion processes local time minimax estimation nonparametric regression wavelets on the internal wavelet orthonormal bases

Citation

Hofmann, Marc. Lp estimation of the diffusion coefficient. Bernoulli 5 (1999), no. 3, 447--481. https://projecteuclid.org/euclid.bj/1172617199


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