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

We consider stochastic UL and LU block factorizations of the one-steptransition probability matrix for a discrete-time quasi-birth-and-deathprocess, namely a stochastic block tridiagonal matrix. The simpler case ofrandom walks with only nearest neighbors transitions gives a unique LUfactorization and a one-parameter family of factorizations in the UL case. Theblock structure considered here yields many more possible factorizationsresulting in a much enlarged class of potential applications. By reversing theorder of the factors (also known as a Darboux transformation) we get newfamilies of quasi-birth-and-death processes where it is possible to identifythe matrix-valued spectral measures in terms of a Geronimus (UL) or aChristoffel (LU) transformation of the original one. We apply our results toone example going with matrix-valued Jacobi polynomials arising in grouprepresentation theory. We also give urn models for some particular cases.

Stochastic Darboux transformations for quasi-birth-and-death processes and urn models