1. MATRIX MEASURES AND RANDOM WALKS WITH A BLOCK TRIDIAGONAL TRANSITION MATRIX.
- Author
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Dette, Holger, Reuther, Bettina, Studden, W. J., and Zygmunt, M.
- Subjects
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MARKOV processes , *MATRICES (Mathematics) , *CHEBYSHEV polynomials , *MATHEMATICAL analysis , *NUMERICAL analysis , *INTEGRAL calculus - Abstract
In this paper we study the connection between matrix measures and random walks with a block tridiagonal transition matrix. We derive sufficient conditions such that the blocks of the n-step block tridiagonal 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. [ABSTRACT FROM AUTHOR]
- Published
- 2007
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