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Studden, W. J.
Reuther, Bettina
Dette, Holger
Zygmunt, M.
Year of Publication: 
Series/Report no.: 
Technical Report / Universität Dortmund, SFB 475 Komplexitätsreduktion in Multivariaten Datenstrukturen 2005,25
In this paper we study the connection between matrix measures and random walks with a tridiagonal block transition matrix. We derive sufficient conditions such that the blocks of the n-step 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.
Markov chain
block tridiagonal transition matrix
spectral measure
matrix measure
quasi birth and death processes
canonical moments
Document Type: 
Working Paper

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