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Weak convergence towards two independent Gaussian processes from a unique Poisson process

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Abstract

We consider two independent Gaussian processes that admit a representation in terms of a stochastic integral of a deterministic kernel with respect to a standard Wiener process. In this paper we construct two families of processes, from a unique Poisson process, the finite dimensional distributions of which converge in law towards the finite dimensional distributions of the two independent Gaussian processes.

As an application of this result we obtain families of processes that converge in law towards fractional Brownian motion and subfractional Brownian motion.

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Authors and Affiliations

  1. Departament de Matemàtiques, Universitat Autònoma de Barcelona, 08193, Bellaterra, (Spain)

    Xavier Bardina & David Bascompte

Authors
  1. Xavier Bardina
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  2. David Bascompte
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Correspondence to Xavier Bardina.

Additional information

The authors are partially supported by MECFeder Grant MTM2006-06427.

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Bardina, X., Bascompte, D. Weak convergence towards two independent Gaussian processes from a unique Poisson process. Collect. Math. 61, 191–204 (2010). https://doi.org/10.1007/BF03191241

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  • DOI: https://doi.org/10.1007/BF03191241

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