A note on the invariant distribution of a quasi-birth-and-death process

Abstract

The aim of this paper is to give an explicit formula of the invariant distribution of a quasi-birth-and-death process in terms of the block entries of the transition probability matrix using a matrix-valued orthogonal polynomials approach. We will show that the invariant distribution can be computed using the squared norms of the corresponding matrix-valued orthogonal polynomials, no matter if they are or not diagonal matrices. We will give an example where the squared norms are not diagonal matrices, but nevertheless we can compute its invariant distribution.

References in corpus (1)

• Random walks and orthogonal polynomials: some challenges

Cited by in corpus (1)

• Deformation of matrix-valued orthogonal polynomials related to Gelfand pairs