Open Access
Translator Disclaimer
October 1996 Transforming random elements and shifting random fields
Hermann Thorisson
Ann. Probab. 24(4): 2057-2064 (October 1996). DOI: 10.1214/aop/1041903217

Abstract

Consider a locally compact second countable topological transformation group acting measurably on an arbitrary space. We show that the distributions of two random elements X and $X'$ in this space agree on invariant sets if and only if there is a random transformation $\Gamma$ such that $\Gamma X$ has the same distribution as $X'$. Applying this to random fields in d dimensions under site shifts, we show further that these equivalent claims are also equivalent to site-average total variation convergence. This convergence result extends to amenable groups.

Citation

Download Citation

Hermann Thorisson. "Transforming random elements and shifting random fields." Ann. Probab. 24 (4) 2057 - 2064, October 1996. https://doi.org/10.1214/aop/1041903217

Information

Published: October 1996
First available in Project Euclid: 6 January 2003

zbMATH: 0879.60051
MathSciNet: MR1415240
Digital Object Identifier: 10.1214/aop/1041903217

Subjects:
Primary: 60B99 , 60G60

Keywords: coupling , invariant $\omega$-algebra , Random field , Topological transformation group , Total variation

Rights: Copyright © 1996 Institute of Mathematical Statistics

JOURNAL ARTICLE
8 PAGES


SHARE
Vol.24 • No. 4 • October 1996
Back to Top