ESAIM: Probability and Statistics (ESAIM: P&S)

ESAIM: P&S, March 2007, Vol. 11, pp. 115-146
DOI: 10.1051/ps:2007010

Approximation of the fractional Brownian sheet VIA Ornstein-Uhlenbeck sheet

Laure Coutin and Monique Pontier

Université Paul Sabatier, 31062 Toulouse cedex 04; Laure.Coutin@lsp.ups-tlse.fr; Monique.Pontier@lsp.ups-tlse.fr

(Received November 16, 2005. Revised April 21 and July 22, 2006. Published online 31 March 2007.)

Abstract
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 $(\alpha_1,\alpha_2)\in ]0,1[^2,\alpha_i\neq\frac.$ Finally, the approximation process is iterative on the quarter plane $\mathbb{R} _+^2.$ A sample of such simulations can be used to test estimators of the parameters $\alpha_i, i=1,2.$

Mathematics Subject Classification. 60G60, 60G15, 62M40.

Key words: random field simulation and approximation, anisotropic fractional Brownian sheet.

© EDP Sciences, SMAI 2007