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Recurrence and Transience of Critical Branching Processes in Random Environment with Immigration and an Application to Excited Random Walks

Part of: Special processes Markov processes

Published online by Cambridge University Press:  22 February 2016

Elisabeth Bauernschubert
Elisabeth Bauernschubert*
Affiliation:
University of Tuebingen
*
∗ Postal address: Mathematisches Institut, Eberhard Karls Universität Tübingen, Auf der Morgenstelle 10, 72076 Tübingen, Germany. Email address: [email protected]
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Abstract

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We establish recurrence and transience criteria for critical branching processes in random environments with immigration. These results are then applied to the recurrence and transience of a recurrent random walk in a random environment on ℤ disturbed by cookies inducing a drift to the right of strength 1.

Keywords

Critical branching process in a random environment with immigrationexcited random walk in a random environmentcookies of strength 1recurrencetransience

MSC classification

Primary: 60J80: Branching processes (Galton-Watson, birth-and-death, etc.)
Secondary: 60J85: Applications of branching processes 60K37: Processes in random environments
Type
General Applied Probability
Information
Advances in Applied Probability , Volume 46 , Issue 3 , September 2014 , pp. 687 - 703
Copyright
© Applied Probability Trust 

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