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Strong approximations of Brownian sheet by uniform transport processes

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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.

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Authors and Affiliations

  1. Departament de Matemàtiques, Facultat de Ciències Edifici C, Universitat Autònoma de Barcelona, 08193, Bellaterra, Spain

    Xavier Bardina

  2. Dipartimento di Matematica “Tullio Levi-Civita”, Università degli Studi di Padova, Via Trieste 63, 35121, Padua, Italy

    Marco Ferrante

  3. Departament de Matemàtiques i Informàtica, Universitat de Barcelona, Gran Via 585, 08007, Barcelona, Spain

    Carles Rovira

Authors
  1. Xavier Bardina
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  2. Marco Ferrante
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  3. Carles Rovira
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Correspondence to Xavier Bardina.

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X. Bardina and C. Rovira are supported by the grant PGC2018-097848-B-I00 from Ministerio de Ciencia, Innovación y Universidades.

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Bardina, X., Ferrante, M. & Rovira, C. Strong approximations of Brownian sheet by uniform transport processes. Collect. Math. 71, 319–329 (2020). https://doi.org/10.1007/s13348-019-00263-4

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  • DOI: https://doi.org/10.1007/s13348-019-00263-4

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