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

In this paper, we derive a simple drift condition for the stability of aclass of two-dimensional Markov processes, for which one of the coordinates(also referred to as the {\em phase} for convenience) has a well understoodbehaviour dependent on the other coordinate (also referred as {\em level}). Thefirst (phase) component's transitions may depend on the second component andare only assumed to be eventually independent. The second (level) component haspartially bounded jumps and it is assumed to have a negative drift given thatthe first one is in its stationary distribution. The results presented in thiswork can be applied to processes of the QBD (quasi-birth-and-death) type on thequarter- and on the half-plane, where the phase and level are interdependent.Furthermore, they provide an off-the-shelf technique to tackle stability issuesfor a class of two-dimensional Markov processes. These results set the steppingstones towards closing the existing gap in the literature of deriving easilyverifiable conditions/criteria for two-dimensional processes with unboundedjumps and interdependence between the two components.

Stability of two-dimensional Markov processes, with an application to QBD processes with an infinite number of phases