Cutpoints of non-homogeneous random walks

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

Latin American Journal of Probability and Mathematical Statistics, 19, March 2022, 493–510. DOI: 10.30757/ALEA.v19-19

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 $\mathbb{R}^d$, $d \geq 2$, possess infinitely many separating annuli, generalizing previous results on spatially homogeneous random walks.