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On the total reward variance for continuous-time Markov reward chains

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: nivd@fee.uva.nl
∗∗Postal address: Institute of Information Theory and Automation, Academy of Sciences of the Czech Republic, PO Box 18, Pod Vodárenskou věží 4, 182 08 Prague 8, Czech Republic. Email address: sladky@utia.cas.cz
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Abstract

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As an extension of the discrete-time case, this note investigates the variance of the total cumulative reward for continuous-time Markov reward chains with finite state spaces. The results correspond to discrete-time results. In particular, the variance growth rate is shown to be asymptotically linear in time. Expressions are provided to compute this growth rate.

Keywords

Continuous-time Markov reward chainvariance of cumulative rewardasymptotic behaviouruniformization

MSC classification

Primary: 90C47: Minimax problems
Secondary: 60J27: Continuous-time Markov processes on discrete state spaces
Type
Research Papers
Information
Journal of Applied Probability , Volume 43 , Issue 4 , December 2006 , pp. 1044 - 1052
Copyright
© Applied Probability Trust 2006 

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