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Exact aggregation of absorbing Markov processes using the quasi-stationary distribution

Part of: Markov processes

Published online by Cambridge University Press:  14 July 2016

James Ledoux ,
Gerardo Rubino  and
Bruno Sericola
James Ledoux
Affiliation:
IRISA-INRIA
Gerardo Rubino
Affiliation:
IRISA-INRIA
Bruno Sericola*
Affiliation:
IRISA-INRIA
*
∗ Postal address for all authors: IRISA-INRIA, Campus de Beaulieu 35042 Rennes, France.
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Abstract

We characterize the conditions under which an absorbing Markovian finite process (in discrete or continuous time) can be transformed into a new aggregated process conserving the Markovian property, whose states are elements of a given partition of the original state space. To obtain this characterization, a key tool is the quasi-stationary distribution associated with absorbing processes. It allows the absorbing case to be related to the irreducible one. We are able to calculate the set of all initial distributions of the starting process leading to an aggregated homogeneous Markov process by means of a finite algorithm. Finally, it is shown that the continuous-time case can always be reduced to the discrete one using the uniformization technique.

Keywords

WEAK LUMPABILITYUNIFORMIZATION

MSC classification

Primary: 60J10: Markov chains (discrete-time Markov processes on discrete state spaces)
Secondary: 60J27: Continuous-time Markov processes on discrete state spaces
Type
Research Papers
Information
Journal of Applied Probability , Volume 31 , Issue 3 , September 1994 , pp. 626 - 634
Copyright
Copyright © Applied Probability Trust 1994 

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Footnotes

This work was partially supported by the Regional Council of Britanny under Grant 290C2010031305061.

References

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