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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.
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Richard A. Holley
Thomas M. Liggett
The Annals of Probability
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Holley et al. (Fri,) studied this question.
www.synapsesocial.com/papers/69d9ab73387cf706986850a8 — DOI: https://doi.org/10.1214/aop/1176996306
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