Open Access
Translator Disclaimer
July, 1986 Characterisations of Set-Indexed Brownian Motion and Associated Conditions for Finite-Dimensional Convergence
Charles M. Goldie, Priscilla E. Greenwood
Ann. Probab. 14(3): 802-816 (July, 1986). DOI: 10.1214/aop/1176992439

Abstract

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.

Citation

Download Citation

Charles M. Goldie. Priscilla E. Greenwood. "Characterisations of Set-Indexed Brownian Motion and Associated Conditions for Finite-Dimensional Convergence." Ann. Probab. 14 (3) 802 - 816, July, 1986. https://doi.org/10.1214/aop/1176992439

Information

Published: July, 1986
First available in Project Euclid: 19 April 2007

zbMATH: 0603.60017
MathSciNet: MR841585
Digital Object Identifier: 10.1214/aop/1176992439

Subjects:
Primary: 60F05
Secondary: 60B10 , 60G48 , 62E10

Keywords: Brownian motion , characterisation , finite-dimensional convergence , lattice-indexed random variables , mixing random variables , partial-sum processes , set-indexed processes , Wiener process

Rights: Copyright © 1986 Institute of Mathematical Statistics

JOURNAL ARTICLE
15 PAGES


SHARE
Vol.14 • No. 3 • July, 1986
Back to Top