COSTA, Oswaldo Luiz Do Valle; DUFOUR, François

doi:10.1080/17442508.2018.1546305

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COSTA, Oswaldo Luiz Do Valle
Universidade de São Paulo = University of São Paulo [USP]

DUFOUR, François
Institut Polytechnique de Bordeaux [Bordeaux INP]
Quality control and dynamic reliability [CQFD]
Institut de Mathématiques de Bordeaux [IMB]

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Stochastics: An International Journal of Probability and Stochastic Processes. 2019, vol. 91, n° 6, p. 817-835

Taylor & Francis: STM, Behavioural Science and Public Health Titles

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The main goal of this paper is to study the infinite-horizon long run average continuous-time optimal control problem of piecewise deterministic Markov processes (PDMPs) with the control acting continuously on the jump intensity λ and on the transition measure Q of the process. We provide conditions for the existence of a solution to an integro-differential optimality inequality, the so called Hamilton-Jacobi-Bellman (HJB) equation, and for the existence of a deterministic stationary optimal policy. These results are obtained by using the so-called vanishing discount approach, under some continuity and compactness assumptions on the parameters of the problem, as well as some non-explosive conditions for the process.< Leer menos

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Continuous-time Markov decision process

Piecewise deterministic Markov process

Hamilton-Jacobi-Bellman inequality

Continuous control

Average control

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Hamilton-Jacobi-Bellman inequality for the average control of piecewise deterministic Markov processes

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