# Approximation of the fractional Brownian sheet VIA Ornstein-Uhlenbeck sheet

• Volume: 11, page 115-146
• ISSN: 1292-8100

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## Abstract

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A stochastic “Fubini” lemma and an approximation theorem for integrals on the plane are used to produce a simulation algorithm for an anisotropic fractional Brownian sheet. The convergence rate is given. These results are valuable for any value of the Hurst parameters $\left({\alpha }_{1},{\alpha }_{2}\right)\in {\right]0,1\left[}^{2},{\alpha }_{i}\ne \frac{1}{2}.$ Finally, the approximation process is iterative on the quarter plane ${ℝ}_{+}^{2}.$ A sample of such simulations can be used to test estimators of the parameters αi,i = 1,2.

## How to cite

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Coutin, Laure, and Pontier, Monique. "Approximation of the fractional Brownian sheet VIA Ornstein-Uhlenbeck sheet." ESAIM: Probability and Statistics 11 (2007): 115-146. <http://eudml.org/doc/250120>.

@article{Coutin2007,
abstract = { A stochastic “Fubini” lemma and an approximation theorem for integrals on the plane are used to produce a simulation algorithm for an anisotropic fractional Brownian sheet. The convergence rate is given. These results are valuable for any value of the Hurst parameters $(\alpha_1,\alpha_2)\in ]0,1[^2,\alpha_i\neq\frac\{1\}\{2\}.$ Finally, the approximation process is iterative on the quarter plane $\mathbb \{R\}_+^2.$ A sample of such simulations can be used to test estimators of the parameters αi,i = 1,2. },
author = {Coutin, Laure, Pontier, Monique},
journal = {ESAIM: Probability and Statistics},
keywords = {random field simulation and approximation; anisotropic fractional Brownian sheet.; anisotropic fractional Brownian sheet},
language = {eng},
month = {3},
pages = {115-146},
publisher = {EDP Sciences},
title = {Approximation of the fractional Brownian sheet VIA Ornstein-Uhlenbeck sheet},
url = {http://eudml.org/doc/250120},
volume = {11},
year = {2007},
}

TY - JOUR
AU - Coutin, Laure
AU - Pontier, Monique
TI - Approximation of the fractional Brownian sheet VIA Ornstein-Uhlenbeck sheet
JO - ESAIM: Probability and Statistics
DA - 2007/3//
PB - EDP Sciences
VL - 11
SP - 115
EP - 146
AB - A stochastic “Fubini” lemma and an approximation theorem for integrals on the plane are used to produce a simulation algorithm for an anisotropic fractional Brownian sheet. The convergence rate is given. These results are valuable for any value of the Hurst parameters $(\alpha_1,\alpha_2)\in ]0,1[^2,\alpha_i\neq\frac{1}{2}.$ Finally, the approximation process is iterative on the quarter plane $\mathbb {R}_+^2.$ A sample of such simulations can be used to test estimators of the parameters αi,i = 1,2.
LA - eng
KW - random field simulation and approximation; anisotropic fractional Brownian sheet.; anisotropic fractional Brownian sheet
UR - http://eudml.org/doc/250120
ER -

## References

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