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Strong approximations of Brownian sheet by uniform transport processes

  • Xavier BardinaEmail author
  • Marco Ferrante
  • Carles Rovira
Article
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Abstract

Many years ago, Griego, Heath and Ruiz-Moncayo proved that it is possible to define realizations of a sequence of uniform transport processes that converges almost surely to the standard Brownian motion, uniformly on the unit time interval. In this paper we extend their results to the multi parameter case. We begin constructing a family of processes, starting from a set of independent standard Poisson processes, that has realizations that converge almost surely to the Brownian sheet, uniformly on the unit square. At the end the extension to the d-parameter Wiener processes is presented.

Notes

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© Universitat de Barcelona 2019

Authors and Affiliations

  1. 1.Departament de Matemàtiques, Facultat de Ciències Edifici CUniversitat Autònoma de BarcelonaBellaterraSpain
  2. 2.Dipartimento di Matematica “Tullio Levi-Civita”Università degli Studi di PadovaPaduaItaly
  3. 3.Departament de Matemàtiques i InformàticaUniversitat de BarcelonaBarcelonaSpain

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