Matrix Measures and Random Walks with a Block Tridiagonal Transition Matrix
نویسندگان
چکیده
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.
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عنوان ژورنال:
- SIAM J. Matrix Analysis Applications
دوره 29 شماره
صفحات -
تاریخ انتشار 2006