## Bernoulli

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

### Lp estimation of the diffusion coefficient

Marc Hofmann

#### 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 $( 1≤p<+∞)$ 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

https://projecteuclid.org/euclid.bj/1172617199

Mathematical Reviews number (MathSciNet)
MR1693608

#### 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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