English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Plus annual

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Plus monthly

Global: Zendy Tools annual

Global: Zendy Tools monthly

Global: Zendy Free Plan

We consider a random walk on the first quadrant of the square lattice, whoseincrement law is, roughly speaking, homogeneous along a finite number ofhalf-lines near each of the two boundaries, and hence essentially specified byfinitely-many transition laws near each boundary, together with an interiortransition law that applies at sufficient distance from both boundaries. Undermild assumptions, in the (most subtle) setting in which the mean drift in theinterior is zero, we classify recurrence and transience and provide power-lawbounds on tails of passage times; the classification depends on the interiorcovariance matrix, the (finitely many) drifts near the boundaries, andstationary distributions derived from two one-dimensional Markov chainsassociated to each of the two boundaries. As an application, we considerreflected random walks related to multidimensional variants of the Lindleyprocess, for which the recurrence question was studied recently by Peign\'e andWoess (Ann. Appl. Probab., vol. 31, 2021) using different methods, but forwhich no previous quantitative results on passage-times appear to be known.

Passage-times for partially-homogeneous reflected random walks on the quadrant