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Cutpoints of non-homogeneous random walks

Lo, Chak Hei; Menshikov, Mikhail; Wade, Andrew R; (2022) Cutpoints of non-homogeneous random walks. ALEA: Latin American Journal of Probability and Mathematical Statistics , 19 (1) pp. 493-510. 10.30757/ALEA.v19-19. Green open access

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Abstract

We give conditions under which near-critical stochastic processes on the half-line have infinitely many or finitely many cutpoints, generalizing existing results on nearest-neighbour random walks to adapted processes with bounded increments satisfying appropriate conditional increment moments conditions. We apply one of these results to deduce that a class of transient zero-drift Markov chains in (Formula presented), d > 2, possess infinitely many separating annuli, generalizing previous results on spatially homogeneous random walks.

Type: Article
Title: Cutpoints of non-homogeneous random walks
Open access status: An open access version is available from UCL Discovery
DOI: 10.30757/ALEA.v19-19
Publisher version: https://doi.org/10.30757/ALEA.v19-19
Language: English
Additional information: This version is the version of record. For information on re-use, please refer to the publisher’s terms and conditions.
UCL classification: UCL
UCL > Provost and Vice Provost Offices > UCL BEAMS
UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Maths and Physical Sciences
UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Maths and Physical Sciences > Dept of Statistical Science
URI: https://discovery.ucl.ac.uk/id/eprint/10183767
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