Authors: Dette, Holger
Reuther, Bettina
Studden, W. J.
Zygmunt, M.
Title: Matrix measures and random walks
Language (ISO): en
Abstract: 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.
Subject Headings: block tridiagonal transition matrix
canonical moments
Chebyshev matrix polynomials
Markov chain
matrix measure
quasi birth and death processes
spectral measure
Issue Date: 2005-10-12T06:59:06Z
Appears in Collections:Sonderforschungsbereich (SFB) 475

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