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Numerically Stable Methods for the Computation of Exit Rates in Markov Chains

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  • Juan A. Carrasco

    (Universitat Politècnica de Catalunya)

Abstract

We consider the exit rate from a finite class of transient states of a continuous-time Markov chain and develop numerically stable methods for the computation with bounded from above approximation error of the steady-state exit rate and the time-dependent exit rate. Finally, we develop an also numerically stable method for the computation with bounded from above approximation error of reachable bounds for the time-dependent exit rate which are independent of the initial probability distribution. Applications for the latter include the cyclic analysis of fault-tolerant systems and the analysis of fault-tolerant systems with unobservable up state. The methods compare well from a computational cost point of view with existing alternatives, some with inferior quality regarding error control.

Suggested Citation

  • Juan A. Carrasco, 2016. "Numerically Stable Methods for the Computation of Exit Rates in Markov Chains," Methodology and Computing in Applied Probability, Springer, vol. 18(2), pages 307-334, June.
    • Handle: RePEc:spr:metcap:v:18:y:2016:i:2:d:10.1007_s11009-014-9417-4
    DOI: 10.1007/s11009-014-9417-4
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    References listed on IDEAS

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    1. Donald Gross & Douglas R. Miller, 1984. "The Randomization Technique as a Modeling Tool and Solution Procedure for Transient Markov Processes," Operations Research, INFORMS, vol. 32(2), pages 343-361, April.
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