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

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

2010-06-04

arxiv.org/abs/1006.0759v1

Mathematics

Probability

Scientific paper

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.

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