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What is Fundamental for Markov Chains: First Passage Times, Fundamental Matrices, and Group Generalized Inverses

In: Computations with Markov Chains

Author

Listed:
  • Daniel P. Heyman

    (Bellcore)

  • Dianne P. O’Leary

    (University of Maryland, Department of Computer Science and Institute for Advanced Computer Studies)

Abstract

In this paper we discuss algorithms for computing the fundamental matrix, the group generalized inverse, and the mean and variance of first passage times for discrete time regular Markov chains. The algorithms are based on the GTH algorithm for computing a stationary vector. We show that although all of these quantities can easily be computed from any one of them, the standard algebraic relations do not produce algorithms that preserve low componentwise relative error in each of them.

Suggested Citation

  • Daniel P. Heyman & Dianne P. O’Leary, 1995. "What is Fundamental for Markov Chains: First Passage Times, Fundamental Matrices, and Group Generalized Inverses," Springer Books, in: William J. Stewart (ed.), Computations with Markov Chains, chapter 10, pages 151-161, Springer.
    • Handle: RePEc:spr:sprchp:978-1-4615-2241-6_10
    DOI: 10.1007/978-1-4615-2241-6_10
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