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An example shows that the mentioned condition is important. Finally, without any conditions, the class of so called Poisson-related strategies is also sufficient in the optimization problems. All the results are applicable to the discounted model, they may be useful also for the case of long-run average cost.<\/jats:p>","DOI":"10.1137\/15m1014012","type":"journal-article","created":{"date-parts":[[2015,12,3]],"date-time":"2015-12-03T21:44:26Z","timestamp":1449179066000},"page":"3503-3533","source":"Crossref","is-referenced-by-count":10,"title":["Randomized and Relaxed Strategies in Continuous-Time Markov Decision Processes"],"prefix":"10.1137","volume":"53","author":[{"given":"Alexey","family":"Piunovskiy","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"351","published-online":{"date-parts":[[2015,12,3]]},"reference":[{"key":"atypb1","unstructured":"D. Bertsekas and S. 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Guo and O. Herna\u0301ndez-Lerma,\n                      Continuous-Time Markov Decision Processes: Theory and Applications\n                      , Springer-Verlag, Heidelberg, 2009.","DOI":"10.1007\/978-3-642-02547-1"},{"key":"atypb11","doi-asserted-by":"publisher","DOI":"10.1287\/moor.1100.0477"},{"key":"atypb12","doi-asserted-by":"crossref","unstructured":"O. Herna\u0301ndez-Lerma and J.B. Lasserre,\n                      Discrete-Time Markov Control Processes\n                      , Springer-Verlag, New York, 1996.","DOI":"10.1007\/978-1-4612-0729-0"},{"key":"atypb13","doi-asserted-by":"crossref","unstructured":"O. Herna\u0301ndez-Lerma and J.B. 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Piunovskiy,\n                      Examples in Markov Decision Processes\n                      , Imperial College Press, London, 2013."},{"key":"atypb20","doi-asserted-by":"publisher","DOI":"10.1137\/10081366X"},{"key":"atypb21","doi-asserted-by":"publisher","DOI":"10.1007\/s10957-012-0015-8"},{"key":"atypb22","unstructured":"A. Piunovskiy,\n                      Sufficient classes of strategies in continuous-time Markov decision processes with total expected cost\n                      , in Modern Trends in Controlled Stochastic Processes, A. Piunovskiy, ed., V.II, Luniver Press, Frome, England, forthcoming."},{"key":"atypb23","doi-asserted-by":"crossref","unstructured":"T. Prieto-Rumeau and O. Hernandez-Lerma,\n                      Selected Topics on Continuous-Time Controlled Markov Chains and Markov Games\n                      , Imperial College Press, London, 2012.","DOI":"10.1142\/p829"},{"key":"atypb24","doi-asserted-by":"crossref","unstructured":"H.C. 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