Transforming random elements and shifting random fields
Thorisson, Hermann
Ann. Probab., Tome 24 (1996) no. 2, p. 2057-2064 / Harvested from Project Euclid
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/