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

Juan A. Carrasco ()
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Juan A. Carrasco: Universitat Politècnica de Catalunya

Methodology and Computing in Applied Probability, 2016, vol. 18, issue 2, 307-334

Abstract: 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.

Keywords: Markov processes; Class of transient states; Exit rate; Bounds; Fault-tolerant systems; 60J27; 60J22; 60J28 (search for similar items in EconPapers)
Date: 2016
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DOI: 10.1007/s11009-014-9417-4

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