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2008 Positively and negatively excited random walks on integers, with branching processes
Elena Kosygina, Martin Zerner
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Electron. J. Probab. 13: 1952-1979 (2008). DOI: 10.1214/EJP.v13-572


We consider excited random walks on the integers with a bounded number of i.i.d. cookies per site which may induce drifts both to the left and to the right. We extend the criteria for recurrence and transience by M. Zerner and for positivity of speed by A.-L. Basdevant and A. Singh to this case and also prove an annealed central limit theorem. The proofs are based on results from the literature concerning branching processes with migration and make use of a certain renewal structure.


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Elena Kosygina. Martin Zerner. "Positively and negatively excited random walks on integers, with branching processes." Electron. J. Probab. 13 1952 - 1979, 2008.


Accepted: 6 November 2008; Published: 2008
First available in Project Euclid: 1 June 2016

zbMATH: 1191.60113
MathSciNet: MR2453552
Digital Object Identifier: 10.1214/EJP.v13-572

Primary: 60K35
Secondary: 60J80 , 60K37

Keywords: central limit theorem , excited random walk , Law of Large Numbers , positive and negative cookies , recurrence , Renewal structure , transience

Vol.13 • 2008
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