Studden, W. J.
|Title:||Matrix measures and random walks|
|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|
Chebyshev matrix polynomials
quasi birth and death processes
|Appears in Collections:||Sonderforschungsbereich (SFB) 475|
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