Approximation of the fractional brownian sheet via Ornstein-Uhlenbeck sheet
ESAIM: Probability and Statistics, Tome 11 (2007), pp. 115-146.

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 (α 1 ,α 2 )]0,1[ 2 ,α i 1 2. Finally, the approximation process is iterative on the quarter plane + 2 . A sample of such simulations can be used to test estimators of the parameters α i ,i=1,2.

DOI : 10.1051/ps:2007010
Classification : 60G60, 60G15, 62M40
Mots-clés : random field simulation and approximation, anisotropic fractional brownian sheet
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Coutin, Laure; Pontier, Monique. Approximation of the fractional brownian sheet via Ornstein-Uhlenbeck sheet. ESAIM: Probability and Statistics, Tome 11 (2007), pp. 115-146. doi : 10.1051/ps:2007010. http://archive.numdam.org/articles/10.1051/ps:2007010/

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