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Zbl 0643.60057
Rohlicek, Jan Robin; Willsky, Alan S.
The reduction of perturbed Markov generators: An algorithm exposing the role of transient states. (English)
[J] J. Assoc. Comput. Mach. 35, No.3, 675-696 (1988). ISSN 0004-5411

A new algorithm for the hierarchical aggregation of singularly perturbed finite-state Markov processes is derived. The approach taken bridges the gap between conceptually simple results for a relatively restricted class of processes and the significantly more complex results for the general case. The critical role played by (almost) transient states is exposed, resulting in a straightforward algorithm for the construction of a sequence of aggregate generators associated with various time scales. These generators together provide a uniform asymptotic approximation of the original probability transition function.

MSC 2000:: *60J20 Appl. of discrete Markov processes
60K10 Appl. of renewal theory
65C05 Monte Carlo methods

Keywords: reliability; perturbed finite-state Markov processes; asymptotic approximation

Cited in: Zbl 0658.60102

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