Advances in Applied Probability

Duality and complete convergence for multi-type additive growth models

Eric Foxall

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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.

Article information

Source
Adv. in Appl. Probab., Volume 48, Number 1 (2016), 32-51.

Dates
First available in Project Euclid: 8 March 2016

Permanent link to this document
https://projecteuclid.org/euclid.aap/1457466154

Mathematical Reviews number (MathSciNet)
MR3473566

Zentralblatt MATH identifier
1341.60125

Subjects
Primary: 60J25: Continuous-time Markov processes on general state spaces 92B99: None of the above, but in this section

Keywords
Contact process additive process interacting particle systems

Citation

Foxall, Eric. Duality and complete convergence for multi-type additive growth models. Adv. in Appl. Probab. 48 (2016), no. 1, 32--51. https://projecteuclid.org/euclid.aap/1457466154


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