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

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

2009-05-27

arxiv.org/abs/0905.4360v2

Mathematics

Probability

11 pages

Scientific paper

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 sub-fractional Brownian motion.

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