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Weak convergence towards two independent Gaussian processes from a unique Poisson process
- Source :
- Collectanea Mathematica; 2010: Vol.: 61 Núm.: 2; p. 191-204
- Publication Year :
- 2010
- Publisher :
- Universitat de Barcelona, 2010.
-
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 sub-fractional Brownian motion.<br />Comment: 11 pages
- Subjects :
- Applied Mathematics
General Mathematics
Probability (math.PR)
Mathematical analysis
Ornstein–Uhlenbeck process
Lévy process
Gaussian random field
Stable process
symbols.namesake
Wiener process
60F17
60G15
FOS: Mathematics
symbols
Gaussian function
Applied mathematics
Fractional Poisson process
Gaussian process
Mathematics - Probability
Mathematics
Subjects
Details
- Language :
- Catalan; Valencian
- Database :
- OpenAIRE
- Journal :
- Collectanea Mathematica
- Accession number :
- edsair.doi.dedup.....0a08f6dd1eb7519d3746d8ff9c557fcf