Abstract.
This paper gives conditions for the convergence of the Laurent series expansion for a class of continuous-time controlled Markov chains with possibly unbounded reward (or cost) rates and unbounded transition rates. That series is then used to study several optimization criteria, including n-discount optimality (for n=−1,0,1,...), Blackwell optimality, and the maximization of a certain vector criterion that in particular gives gain and bias optimality.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
Author information
Authors and Affiliations
Corresponding author
Additional information
The research of this author was supported by a grant from the Spanish Secretaría de Estado de Educación y Universidades in cooperation with the European Social Funds.
The research of this author was partially supported by CONACyT Grant 37355-E.
Manuscript received: November 2003/Final version received: July 2004
Rights and permissions
About this article
Cite this article
Prieto-Rumeau, T., Hernández-Lerma, O. The Laurent series, sensitive discount and Blackwell optimality for continuous-time controlled Markov chains. Math Meth Oper Res 61, 123–145 (2005). https://doi.org/10.1007/s001860400393
Issue Date:
DOI: https://doi.org/10.1007/s001860400393
Keywords
- Continuous-time controlled Markov chains (also known as Markov decision processes)
- Laurent series
- Sensitive discount criteria
- Blackwell optimality
- Average reward criteria