Titlebook: Continuous-Time Markov Decision Processes; Borel Space Models a Alexey Piunovskiy,Yi Zhang Book 2020 Springer Nature Switzerland AG 2020 90

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The Average Cost Model,In this chapter, restricted to the class of .-strategies, we consider the following long-run average cost as the performance measure of the system: .for each initial distribution ., . and .-strategy .. Recall that the convention of . for each . is in use.

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Gradual-Impulsive Control Models,The CTMDPs discussed in the previous chapters only allow the decision-maker to control the local characteristics of the process. This chapter considers a more general situation, where the decision-maker can control both the local characteristics and the trajectories of the process.

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Selected Properties of Controlled Processes,nsidered in this book. In Sect.?., we rigorously show that under a natural Markov strategy ., the controlled process . is a Markov pure jump process, with the explicit construction of its transition function being presented.

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Reduction to DTMDP: The Total Cost Model,o solving the control problem for the corresponding Discrete-Time Markov Decision Process (DTMDP). After that, we use the known facts for DTMDP models to obtain the corresponding results for CTMDP models. The necessary information about DTMDPs is in Appendix C. We do not assume that the controlled process . is non-explosive.

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