Approximation of the fractional Brownian sheet VIA Ornstein-Uhlenbeck sheet
Université Paul Sabatier,
31062 Toulouse cedex 04; Laure.Coutin@lsp.ups-tlse.fr; Monique.Pontier@lsp.ups-tlse.fr
Revised: 21 April 2006
Revised: 22 July 2006
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 Finally, the approximation process is iterative on the quarter plane A sample of such simulations can be used to test estimators of the parameters αi,i = 1,2.
Mathematics Subject Classification: 60G60 / 60G15 / 62M40
Key words: random field simulation and approximation / anisotropic fractional Brownian sheet.
© EDP Sciences, SMAI, 2007