Two characterisations are given of the finite-dimensional laws of Brownian motion indexed by an arbitrary class of subsets of the $d$-dimensional unit cube. There are associated conditions for convergence of finite-dimensional laws of a sequence of set-indexed additive processes. These conditions have a more explicit form in the case of set-indexed partial-sum processes based on mixing random variables.
Publié le : 1986-07-14
Classification:
Brownian motion,
characterisation,
finite-dimensional convergence,
lattice-indexed random variables,
mixing random variables,
partial-sum processes,
set-indexed processes,
Wiener process,
60F05,
60B10,
60G48,
62E10
@article{1176992439,
author = {Goldie, Charles M. and Greenwood, Priscilla E.},
title = {Characterisations of Set-Indexed Brownian Motion and Associated Conditions for Finite-Dimensional Convergence},
journal = {Ann. Probab.},
volume = {14},
number = {4},
year = {1986},
pages = { 802-816},
language = {en},
url = {http://dml.mathdoc.fr/item/1176992439}
}
Goldie, Charles M.; Greenwood, Priscilla E. Characterisations of Set-Indexed Brownian Motion and Associated Conditions for Finite-Dimensional Convergence. Ann. Probab., Tome 14 (1986) no. 4, pp. 802-816. http://gdmltest.u-ga.fr/item/1176992439/