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 Tools annual

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 Tools monthly

Global: Zendy Plus monthly

Presents the access of premium content as premium feature

Premium Content

Global: Zendy Plus annual

Global: Zendy Free Plan

In this paper, we analyse a sub-class of two-dimensional homogeneous nearestneighbour (simple) random walk restricted on the lattice using the matrixgeometric approach. In particular, we first present an alternative approach forthe calculation of the stability condition, extending the result of Neuts driftconditions [30] and connecting it with the result of Fayolle et al. which isbased on Lyapunov functions [13]. Furthermore, we consider the sub-class ofrandom walks with equilibrium distributions given as series of product-formsand, for this class of random walks, we calculate the eigenvalues and thecorresponding eigenvectors of the infinite matrix $\mathbf{R}$ appearing in thematrix geometric approach. This result is obtained by connecting and extendingthree existing approaches available for such an analysis: the matrix geometricapproach, the compensation approach and the boundary value problem method. Inthis paper, we also present the spectral properties of the infinite matrix$\mathbf{R}$.

Matrix geometric approach for random walks: stability condition and equilibrium distribution