Stochastic Optimal Control: The Discrete-Time Case
Stochastic Optimal Control: The Discrete-Time Case
Continuous Time Discounted Jump Markov Decision Processes: A Discrete-Event Approach
Mathematics of Operations Research
Continuous-Time Markov Decision Processes with Discounted Rewards: The Case of Polish Spaces
Mathematics of Operations Research
Brief paper: Towards the optimal control of Markov chains with constraints
Automatica (Journal of IFAC)
Mathematics of Operations Research
Controlled stochastic jump processes
MMES'10 Proceedings of the 2010 international conference on Mathematical models for engineering science
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This paper deals with constrained discounted continuous-time Markov decision processes, also known as controlled jump Markov processes, with Borel state and action spaces. Under some conditions imposed on the primitives, allowing unbounded transition rates and unbounded (from both above and below) cost rates, first, we study the space of occupation measures. Then we reformulate the original problem as a linear program over the space of those measures and undertake the duality analysis. Finally, under some compactness-continuity conditions, we show the existence of a stationary optimal policy out of the class of randomized history-dependent policies.