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A note on uniformization for dynamic non-negative systems

Part of: Markov processes

Published online by Cambridge University Press:  14 July 2016

Nico M. van Dijk  and
Karel Sladký
Nico M. van Dijk*
Affiliation:
University of Amsterdam
Karel Sladký*
Affiliation:
Institute of Information Theory and Automation, Prague
*
∗Postal address: Department of Economic Sciences and Econometrics, University of Amsterdam, Roetersstraat 11, 1018 WB Amsterdam, The Netherlands. Email address: sladky@utia.cas.cz
∗∗Postal address: Institute of Information Theory and Automation, Academy of Sciences of the Czech Republic, PO Box 18, 182 08 Prague 8, Czech Republic. Email address: sladky@utia.cas.cz.
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Abstract

The classical technique of uniformization (or randomization) for bounded continuous-time Markov chains and Markov reward structures is extended to dynamic systems generated by arbitrary non-negative generators. Most notably, these include so-called input-output models in economic analysis. The results are of practical interest for both computational and theoretical purposes. Particularly, the recursive computation and the limiting behaviour of cumulative reward structures for non-negative dynamic systems is concluded as a special application. Two numerical examples are included to illustrate the conditions and the results.

Keywords

Uniformizationstochastic generator matrixnon-negative generator matrixinput-output models

MSC classification

Primary: 60J27: Continuous-time Markov processes on discrete state spaces
Type
Research Papers
Information
Journal of Applied Probability , Volume 37 , Issue 2 , June 2000 , pp. 329 - 341
Copyright
Copyright © by the Applied Probability Trust 2000 

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