A d-dimensional Brownian motion as a weak limit from a one-dimensional Poisson process

A d-dimensional Brownian motion as a weak limit from a one-dimensional Poisson process

Xavier Bardina and Carles Rovira

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

Abstract

We show how from an unique standard Poisson process we can build a family of processes that converges in law to a d-dimensional standard Brownian motion for any $d\geq1$.

Keywords: d-dimensional Brownian motion, weak approximations, Poisson process

Published in:

Lithuanian Mathematical Journal

53 (1)

17-26

2013