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Duality and complete convergence for multi-type additive growth models

Part of: Mathematical biology in general Markov processes

Published online by Cambridge University Press:  24 March 2016

Eric Foxall
Eric Foxall*
Affiliation:
University of Victoria
*
* Postal address: Department of Mathematics and Statistics, University of Victoria, PO Box 3060, STN CSC, Victoria, BC, V8W 3R4, Canada. Email address: e.t.foxall@gmail.com
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Abstract

We consider a class of multi-type particle systems whose structure is similar to that of a contact process and show that additivity is equivalent to the existence of a dual process, extending a result of Harris. We prove a necessary and sufficient condition for the model to preserve positive correlations. We then show that complete convergence on Zd holds for a large subclass of models including the two-stage contact process and a household model, and give examples.

Keywords

Contact processadditive processinteracting particle systems

MSC classification

Primary: 60J25: Continuous-time Markov processes on general state spaces 92B99: None of the above, but in this section
Type
Research Article
Information
Advances in Applied Probability , Volume 48 , Issue 1 , March 2016 , pp. 32 - 51
Copyright
Copyright © Applied Probability Trust 2016 

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