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Central limit theorems for biased randomly trapped random walks on Z

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Bowditch, Adam (2019) Central limit theorems for biased randomly trapped random walks on Z. Stochastic Processes and their Applications, 129 (3). pp. 740-770. doi:10.1016/j.spa.2018.03.017

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Official URL: http://dx.doi.org/10.1016/j.spa.2018.03.017

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Abstract

We prove CLTs for biased randomly trapped random walks in one dimension. By considering a sequence of regeneration times, we will establish an annealed invariance principle under a second moment condition on the trapping times. In the quenched setting, an environment dependent centring is necessary to achieve a central limit theorem. We determine a suitable expression for this centring. As our main motivation, we apply these results to biased walks on subcritical Galton–Watson trees conditioned to survive for a range of bias values.

Item Type: Journal Article
Subjects: Q Science > QA Mathematics
Divisions: Faculty of Science > Statistics
Library of Congress Subject Headings (LCSH): Central limit theorem, Random walks (Mathematics), Stochastic processes
Journal or Publication Title: Stochastic Processes and their Applications
Publisher: Elsevier Science BV
ISSN: 0304-4149
Official Date: March 2019
Dates:
DateEvent
March 2019Published
5 April 2018Available
26 March 2018Accepted
Volume: 129
Number: 3
Page Range: pp. 740-770
DOI: 10.1016/j.spa.2018.03.017
Status: Peer Reviewed
Publication Status: Published
Access rights to Published version: Open Access
RIOXX Funder/Project Grant:
Project/Grant IDRIOXX Funder NameFunder ID
EP/H023364/1[EPSRC] Engineering and Physical Sciences Research Councilhttp://dx.doi.org/10.13039/501100000266

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