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Matrix measures and random walks

Author

Listed:
  • Studden, W. J.
  • Reuther, Bettina
  • Dette, Holger
  • Zygmunt, M.

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.

Suggested Citation

  • Studden, W. J. & Reuther, Bettina & Dette, Holger & Zygmunt, M., 2005. "Matrix measures and random walks," Technical Reports 2005,25, Technische Universität Dortmund, Sonderforschungsbereich 475: Komplexitätsreduktion in multivariaten Datenstrukturen.
    • Handle: RePEc:zbw:sfb475:200525
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