A theorem exhibiting the duality between certain infinite systems of interacting stochastic processes and a type of branching process is proved. This duality is then used to study the ergodic properties of the infinite system. In the case of the vector model a complete understanding of the ergodic behavior is obtained.
Publié le : 1975-08-14
Classification:
Infinite particle system,
ergodic theorem,
branching process with interference,
Markov chain,
harmonic function,
60K35,
60J10
@article{1176996306,
author = {Holley, Richard A. and Liggett, Thomas M.},
title = {Ergodic Theorems for Weakly Interacting Infinite Systems and the Voter Model},
journal = {Ann. Probab.},
volume = {3},
number = {6},
year = {1975},
pages = { 643-663},
language = {en},
url = {http://dml.mathdoc.fr/item/1176996306}
}
Holley, Richard A.; Liggett, Thomas M. Ergodic Theorems for Weakly Interacting Infinite Systems and the Voter Model. Ann. Probab., Tome 3 (1975) no. 6, pp. 643-663. http://gdmltest.u-ga.fr/item/1176996306/