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

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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 (α 1 ,α 2 )∈]0,1[ 2 ,α i ≠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 α i ,i=1,2.

DOI : 10.1051/ps:2007010
Classification : 60G60, 60G15, 62M40
Keywords: random field simulation and approximation, anisotropic fractional brownian sheet 
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     title = {Approximation of the fractional brownian sheet via {Ornstein-Uhlenbeck} 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

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