Weak approximation of the Wiener process from a Poisson process: the multidimensional parameter set case.

Xavier Bardina, Maria Jolis, Carles Rovira

Departament de Matemàtiques, Edifici C, Universitat Auṭnoma de Barcelona, 08193 Bellaterra, Barcelona, Spain
Facultat de Matemàtiques, Universitat de Barcelona, Gran Via 585, 08007 Barcelona, Spain

Abstract
We give an approximation in law of the d-parameter Wiener process by processes constructed from a Poisson process with parameter in R^d. This approximation is an extension of previous results of Stroock (1982) and Bardina and Jolis.

Published in: Statistics and Probability Letters, 50 (3), 245-255, 2000