Matrix measures and random walks

Holger Dette; Bettina Reuther; William J. Studden; Mirosława Zygmunt

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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Year of publication:	2005
Authors:	Dette, Holger ; Reuther, Bettina ; Studden, William J. ; Zygmunt, Mirosława
Publisher:	Dortmund : Univ., SFB 475
Subject:	Markov-Kette \| Markov chain \| Theorie \| Theory \| Lineare Algebra \| Linear algebra \| Random Walk \| Random walk