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Zeitschrift für Operations Research

, Volume 39, Issue 2, pp 131–155 | Cite as

Controlled Markov processes on the infinite planning horizon: Weighted and overtaking cost criteria

  • Emmanuel Fernández-Gaucherand
  • Mrinal K. Ghosh
  • Steven I. Marcus
Articles

Abstract

Stochastic control problems for controlled Markov processes models with an infinite planning horizon are considered, under some non-standard cost criteria. The classical discounted and average cost criteria can be viewed as complementary, in the sense that the former captures the short-time and the latter the long-time performance of the system. Thus, we study a cost criterion obtained as weighted combinations of these criteria, extending to a general state and control space framework several recent results by Feinberg and Shwartz, and by Krass et al. In addition, a functional characterization is given for overtaking optimal policies, for problems with countable state spaces and compact control spaces; our approach is based on qualitative properties of the optimality equation for problems with an average cost criterion.

Key words

Controlled Markov Processes Infinite Planning Horizon Weighted and Overtaking Cost Criteria 

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Copyright information

© Physica-Verlag 1994

Authors and Affiliations

  • Emmanuel Fernández-Gaucherand
    • 1
  • Mrinal K. Ghosh
    • 2
  • Steven I. Marcus
    • 3
  1. 1.Systems & Industrial Engineering DepartmentThe University of ArizonaTucsonUSA
  2. 2.Department of MathematicsIndian Institute of ScienceBangaloreIndia
  3. 3.Institute for Systems Research and Electrical Engineering DepartmentThe University of MarylandCollege ParkUSA

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