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A d-dimensional Brownian motion as a weak limit from a one-dimensional Poisson process |
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| Authors: | Xavier Bardina Carles Rovira |
| Institution: | 1. Departament de Matemàtiques, Edifici C, Universitat Autònoma de Barcelona, 08193, Bellaterra, Barcelona, Spain 2. Facultat de Matemàtiques, Universitat de Barcelona, Gran Via 585, 08007, Barcelona, Spain |
| Abstract: | We show how from a 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 $\geqslant$ 1. |
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