Dette, HolgerReuther, BettinaStudden, W. J.Zygmunt, M.2005-10-122005-10-122005-10-12http://hdl.handle.net/2003/2165310.17877/DE290R-1039In 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.enblock tridiagonal transition matrixcanonical momentsChebyshev matrix polynomialsMarkov chainmatrix measurequasi birth and death processesspectral measure004report