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Discounted Continuous-Time Controlled Markov Chains: Convergence of Control Models

Part of: Markov processes

Published online by Cambridge University Press:  30 January 2018

Tomás Prieto-Rumeau  and
Onésimo Hernández-Lerma
Tomás Prieto-Rumeau*
Affiliation:
Universidad Nacional de Educación a Distancia
Onésimo Hernández-Lerma*
Affiliation:
CINVESTAV-IPN
*
∗ Postal address: Departamento de Estadística, Facultad de Ciencias, Universidad Nacional de Educación a Distancia, Calle Senda del Rey 9, 28040, Madrid, Spain. Email address: [email protected]
∗∗ Postal address: Departamento de Matemáticas, CINVESTAV-IPN, México D.F. 07000, México.
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Abstract

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We are interested in continuous-time, denumerable state controlled Markov chains (CMCs), with compact Borel action sets, and possibly unbounded transition and reward rates, under the discounted reward optimality criterion. For such CMCs, we propose a definition of a sequence of control models {ℳn} converging to a given control model ℳ, which ensures that the discount optimal reward and policies of ℳn converge to those of ℳ. As an application, we propose a finite-state and finite-action truncation technique of the original control model ℳ, which is illustrated by approximating numerically the optimal reward and policy of a controlled population system with catastrophes. We study the corresponding convergence rates.

Keywords

Continuous-time controlled Markov chainapproximation of control modelsdiscount optimality

MSC classification

Primary: 90C40: Markov and semi-Markov decision processes 60J27: Continuous-time Markov processes on discrete state spaces
Type
Research Article
Information
Journal of Applied Probability , Volume 49 , Issue 4 , December 2012 , pp. 1072 - 1090
Copyright
© Applied Probability Trust 

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