Filtered Brownian motions as weak limit of filtered Poisson processes
Decreusefond, Laurent ; Savy, Nicholas
Bernoulli, Tome 11 (2005) no. 1, p. 283-292 / Harvested from Project Euclid
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The main result of this paper is a limit theorem which shows the convergence in law, on a Hölderian space, of filtered Poisson processes (a class of processes which contains shot noise process) to filtered Brownian motion (a class of processes which contains fractional Brownian motion) when the intensity of the underlying Poisson process is increasing. We apply the theory of convergence of Hilbert space valued semimartingales and use a radonification result.
Publié le : 2005-04-14
Classification:  filtered Poisson process,  fractional Brownian motion,  Hilbert-valued martingales,  weak convergence 
@article{1116340295,
     author = {Decreusefond, Laurent and Savy, Nicholas},
     title = {Filtered Brownian motions as weak limit of filtered Poisson processes},
     journal = {Bernoulli},
     volume = {11},
     number = {1},
     year = {2005},
     pages = { 283-292},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1116340295}
}

Decreusefond, Laurent; Savy, Nicholas. Filtered Brownian motions as weak limit of filtered Poisson processes. Bernoulli, Tome 11 (2005) no. 1, pp.  283-292. http://gdmltest.u-ga.fr/item/1116340295/