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One-dimensional branching random walks in a Markovian random environment

Part of: Equilibrium statistical mechanics Markov processes

Published online by Cambridge University Press:  14 July 2016

F. P. Machado  and
S. Yu. Popov
F. P. Machado*
Affiliation:
University of São Paulo
S. Yu. Popov*
Affiliation:
Institute for Problems of Information Transmission, Moscow
*
∗ Postal address: Department of Statistics, Institute of Mathematics and Statistics, University of São Paulo, Rua de Matão 1010, CEP 05508-900, São Paulo, SP, Brazil.
∗ Postal address: Department of Statistics, Institute of Mathematics and Statistics, University of São Paulo, Rua de Matão 1010, CEP 05508-900, São Paulo, SP, Brazil.
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Abstract

We study a one-dimensional supercritical branching random walk in a non-i.i.d. random environment, which considers both the branching mechanism and the step transition. This random environment is constructed using a recurrent Markov chain on a finite or countable state space. Criteria of (strong) recurrence and transience are presented for this model.

Keywords

Branching random walkrandom environmentstrong transiencestrong recurrence

MSC classification

Primary: 60J10: Markov chains (discrete-time Markov processes on discrete state spaces) 60J80: Branching processes (Galton-Watson, birth-and-death, etc.)
Secondary: 82B41: Random walks, random surfaces, lattice animals, etc.
Type
Short Communications
Information
Journal of Applied Probability , Volume 37 , Issue 4 , December 2000 , pp. 1157 - 1163
Copyright
Copyright © by the Applied Probability Trust 2000 

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