We consider the full weak convergence, in appropriate function spaces, of systems of noninteracting particles undergoing critical branching and following a self-similar spatial motion with stationary increments. The limit processes are measure-valued, and are of the super and historical process type. In the case in which the underlying motion is that of a fractional Brownian motion, we obtain a characterization of the limit process as a kind of stochastic integral against the historical process of a Brownian motion defined on the full real line.
Publié le : 1995-04-14
Classification:
Self-similar processes,
fractional Brownian motion,
super process,
historical process,
60F17,
60G17,
60G18,
60H15
@article{1176988287,
author = {Adler, Robert J. and Samorodnitsky, Gennady},
title = {Super Fractional Brownian Motion, Fractional Super Brownian Motion and Related Self-Similar (Super) Processes},
journal = {Ann. Probab.},
volume = {23},
number = {3},
year = {1995},
pages = { 743-766},
language = {en},
url = {http://dml.mathdoc.fr/item/1176988287}
}
Adler, Robert J.; Samorodnitsky, Gennady. Super Fractional Brownian Motion, Fractional Super Brownian Motion and Related Self-Similar (Super) Processes. Ann. Probab., Tome 23 (1995) no. 3, pp. 743-766. http://gdmltest.u-ga.fr/item/1176988287/