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Approximation of the fractional Brownian sheet VIA Ornstein-Uhlenbeck sheet

Published online by Cambridge University Press:  31 March 2007

Laure Coutin  and
Monique Pontier
Laure Coutin
Affiliation:
Université Paul Sabatier, 31062 Toulouse cedex 04; [email protected]; [email protected]
Monique Pontier
Affiliation:
Université Paul Sabatier, 31062 Toulouse cedex 04; [email protected]; [email protected]
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Abstract

A stochastic “Fubini” lemma and an approximation theorem forintegrals on the plane are used to produce a simulation algorithmfor an anisotropic fractional Brownian sheet. The convergence rateis given. These results are valuable for any value of the Hurstparameters $(\alpha_1,\alpha_2)\in ]0,1[^2,\alpha_i\neq\frac{1}{2}.$ Finally, theapproximation processis iterative on the quarter plane $\mathbb {R}_+^2.$ A sample of such simulations can be used to test estimatorsof the parameters αi,i = 1,2.

Keywords

random field simulation and approximationanisotropicfractional Brownian sheet.
Type
Research Article
Information
ESAIM: Probability and Statistics , Volume 11: Special Issue: "Stochastic analysis and mathematical finance" in honor of Nicole El Karoui's 60th birthdaySpecial Issue: "Stochastic analysis and mathematical finance" in honor of Nicole El Karoui's 60th birthday , June 2007 , pp. 115 - 146
Copyright
© EDP Sciences, SMAI, 2007

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