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Criterion for unlimited growth of critical multidimensional stochastic models

Part of: Markov processes

Published online by Cambridge University Press:  11 January 2017

Etienne Adam
Etienne Adam*
Affiliation:
Centre de Mathématiques Appliquées
*
* Postal address: Centre de Mathématiques Appliquées, Ecole Polytechnique, CNRS, Université Paris-Saclay, route de Saclay, 91128 Palaiseau, France. Email address: [email protected]
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Abstract

We give a criterion for unlimited growth with positive probability for a large class of multidimensional stochastic models. As a by-product, we recover the necessary and sufficient conditions for recurrence and transience for critical multitype Galton–Watson with immigration processes and also significantly improve some results on multitype size-dependent Galton–Watson processes.

Keywords

Lyapunov functionmartingalestochastic difference equationcritical multitype Galton–Watson process with immigrationmultitype size-dependent Galton–Watson process

MSC classification

Secondary: 60J80: Branching processes (Galton-Watson, birth-and-death, etc.) 60J10: Markov chains (discrete-time Markov processes on discrete state spaces)
Type
Research Article
Information
Advances in Applied Probability , Volume 48 , Issue 4 , December 2016 , pp. 972 - 988
Copyright
Copyright © Applied Probability Trust 2017 

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