Cutpoints of non-homogeneous random walks

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

20 pages; v2: minor revisions

References in corpus (1)

• A transient Markov chain with finitely many cutpoints

Cited by in corpus (2)

• On a maximum of nearest-neighbor random walk with asymptotically zero drift on lattice of positive half line
• Strong transience for one-dimensional Markov chains with asymptotically zero drifts