Cutpoints of non-homogeneous random walks

Lo, Chak Hei; Menshikov, Mikhail V.; Wade, Andrew R.

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 R d , d ≥ 2, possess infinitely many separating annuli, generalizing previous results on spatially homogeneous random walks.

Citation

Lo, C. H., Menshikov, M. V., & Wade, A. R. (2022). Cutpoints of non-homogeneous random walks. Alea (2006. Online), 19, 493-510. https://doi.org/10.30757/alea.v19-19

• Journal Article Type: Article
• Acceptance Date: Nov 18, 2021
• Online Publication Date: Mar 5, 2022
• Publication Date: 2022
• Deposit Date: Aug 9, 2021
• Publicly Available Date: Nov 22, 2021
• Journal: ALEA - Latin American Journal of Probability and Mathematical Statistics
• Electronic ISSN: 1980-0436
• Publisher: Instituto Nacional de Matemática Pura e Aplicada
• Peer Reviewed: Peer Reviewed
• Volume: 19
• Pages: 493-510
• DOI: https://doi.org/10.30757/alea.v19-19
• Public URL: https://durham-repository.worktribe.com/output/1243303
• Publisher URL: https://alea.impa.br/english/index_v19.htm