Approximation in law to the $d$-parameter fractional Brownian sheet based on the functional invariance principle

Xavier Bardina and Carme Florit

Departament de Matemàtiques, Edifici C, Universitat Autònoma de Barcelona
08193 Bellaterra, Barcelona, Spain

Abstract

We show a result of approximation in law of the $d$-parameter fractional Brownian sheet in the space of the continuous functions on $[0,T]^d$. The construction of these approximations is based on the functional invariance principle.

Keywords: $d$-parameter fractional Brownian sheet; weak convergence; functional invariance principle

Published in: Revista Matemática Iberoamericana, 21 (3) (2005) 1037-1052.