Matrix measures and random walks
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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.
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block tridiagonal transition matrix, canonical moments, Chebyshev matrix polynomials, Markov chain, matrix measure, quasi birth and death processes, spectral measure