Matrix Measures and Random Walks with a Block Tridiagonal Transition Matrix
Holger Dette, Bettina Reuther, W. J. Studden, Marcin J. Zygmunt · SIAM Journal on Matrix Analysis and Applications · 2006
In this paper we study the connection between matrix measures and random walks with a block tridiagonal transition matrix. We derive sufficient conditions such that the blocks of the n‐step block tridiagonal transition matrix of the Markov chain can be represented as integrals with respect to a matrix valued spectral measure. Several stochastic properties of the processes are characterized by means of this matrix measure. In many cases this measure is supported in the interval [‐1,1]. The results are illustrated by several examples including random walks on a grid and the embedded chain of a queuing system.