Weak approximation of the Brownian sheet from a Poisson process in the plane.

Xavier Bardina and Maria Jolis

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

Abstract

In this paper, we show an approximation in law of the Brownian sheet by processes constructed from the Poisson process in the plane. This result has been inspired by a similar result of Stroock in the one parameter case.

Keywords: Two-parameter Wiener process, Two-parameter Poisson process, Weak convergence.

Published in: Bernoulli, 6 (4), 653-665, 2000