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.
Publié le : 1996-10-14
Classification:
Topological transformation group,
random field,
invariant $\omega$-algebra,
total variation,
coupling,
60B99,
60G60
@article{1041903217,
author = {Thorisson, Hermann},
title = {Transforming random elements and shifting random fields},
journal = {Ann. Probab.},
volume = {24},
number = {2},
year = {1996},
pages = { 2057-2064},
language = {en},
url = {http://dml.mathdoc.fr/item/1041903217}
}
Thorisson, Hermann. Transforming random elements and shifting random fields. Ann. Probab., Tome 24 (1996) no. 2, pp. 2057-2064. http://gdmltest.u-ga.fr/item/1041903217/