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On finite long run costs and rewards in infinite Markov chains
Institution:1. Clausthal University of Technology, Department of Applied Stochastics and Operations Research, 38678 Clausthal-Zellerfeld, Germany;2. University of Derby, School of Computing and Mathematics, Derby, DE22 1GB, UK;1. School of Mathematics and Statistics, Guangdong University of Finance & Economics, Guangzhou 510320, PR China;2. Department of Mathematics, Jinan University, Guangzhou 510630, PR China;1. Department of Epidemiology and Biostatistics, School of Public Health, Indiana University Bloomington, 1025 E. 7th street, PH C104, Bloomington, IN, 47405, USA;2. Department of Epidemiology and Biostatistics, University of Georgia, Athens, GA 30602, USA;3. Department of Statistical Science, Southern Methodist University, 3225 Daniel Avenue, PO Box 750332, Dallas, TX 75275-0332, USA;1. School of Mathematics and Statistics, Nanjing Audit University, Nanjing, 210029, China;2. School of Economics and Management, Southeast University, Nanjing, 210096, China;3. Faculty of Mathematics and Informatics, Vilnius University, Naugarduko 24, Vilnius LT-03225, Lithuania;4. Institute of Mathematics and Informatics, Vilnius University, Akademijos 4, Vilnius LT-08663, Lithuania
Abstract:Conditions for the finiteness of long run costs and rewards associated with infinite recurrent Markov chains that may be discrete or continuous in time are considered. Without resorting to results from the theory of Markov processes on general state spaces we provide instructive proofs in the course of which we derive auxiliary results that are of interest in themselves. Potential applications of the finiteness conditions are outlined in order to elucidate their high practical relevance.
Keywords:Infinite Markov chain  Finite long run cost  Finite long run reward  Foster–Lyapunov-type criterion  Drift condition
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