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June, 1978 Limit Theorems for Nonergodic Set-Valued Markov Processes
David Griffeath
Ann. Probab. 6(3): 379-387 (June, 1978). DOI: 10.1214/aop/1176995524

Abstract

Certain Markov processes on the state space of subsets of the integers have $\varnothing$ as a trap, but have an equilibrium $\nu \neq \delta_\varnothing$. In this paper we prove weak convergence to a mixture of $\delta_\varnothing$ and $\nu$ from any initial state for some of these processes. In particular, we prove that the basic symmetric one-dimensional contact process of Harris has only $\delta_\varnothing$ and $\nu$ as extreme equilibria when the infection rate is large enough in comparison to the recovery rate.

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David Griffeath. "Limit Theorems for Nonergodic Set-Valued Markov Processes." Ann. Probab. 6 (3) 379 - 387, June, 1978. https://doi.org/10.1214/aop/1176995524

Information

Published: June, 1978
First available in Project Euclid: 19 April 2007

zbMATH: 0378.60105
MathSciNet: MR488378
Digital Object Identifier: 10.1214/aop/1176995524

Subjects:
Primary: 60K35

Keywords: additive process , associate process , contact process , Infinite particle system

Rights: Copyright © 1978 Institute of Mathematical Statistics

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Vol.6 • No. 3 • June, 1978
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