English

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

Probability 2009-12-15 v1

Abstract

We show how from an unique standard Poisson process we can build a family of processes that converges in law to a dd-dimensional standard Brownian motion for any d1d \ge 1.

Keywords

Cite

@article{arxiv.0912.2457,
  title  = {A $d$-dimensional Brownian motion as a weak limit from a one-dimensional Poisson process},
  author = {Xavier Bardina Carles Rovira},
  journal= {arXiv preprint arXiv:0912.2457},
  year   = {2009}
}
R2 v1 2026-06-21T14:23:09.579Z