Weak convergence to the fractional Brownian sheet and other two parameter Gaussian processes.

Xavier Bardina, Maria Jolis and Ciprian A. Tudor.

Departament de Matemàtiques, Edifici C, Universitat Autònoma de Barcelona
08193 Bellaterra, Barcelona, Spain
Laboratoire de Probabilités; Université Paris 6; 4, Place Jussieu; 75252 Paris Cedex 05; France.

Abstract

We show an approximation in law of the fractional Brownian sheet by processes constructed from the Poisson process in the plane. This result is an extension of a  aper of Bardina and Jolis (2000) where the case of the Brownian sheet was studied.
 
Published in: Statistics and Probabiltity Letters, 65 (4), 317-329, 2003