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random field simulation and approximation

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Approximation of the fractional Brownian sheet VIA Ornstein-Uhlenbeck sheet
Laure Coutin, Monique Pontier
Journal:

ESAIM: Probability and Statistics / Volume 11 / June 2007

Published online by Cambridge University Press:

31 March 2007, pp. 115-146

Print publication:

June 2007
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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.