ANSELMI, Jonatha; DUFOUR, François; PRIETO-RUMEAU, Tomás

doi:10.1017/jpr.2018.36

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ANSELMI, Jonatha
Quality control and dynamic reliability [CQFD]

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

PRIETO-RUMEAU, Tomás
Universidad Nacional de Educación a Distancia [UNED]

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Journal of Applied Probability. 2018-06, vol. 55, n° 02, p. 571-592

Cambridge University press

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In this paper we study the numerical approximation of the optimal long-run average cost of a continuous-time Markov decision process, with Borel state and action spaces, and with bounded transition and reward rates. Our approach uses a suitable discretization of the state and action spaces to approximate the original control model. The approximation error for the optimal average reward is then bounded by a linear combination of coefficients related to the discretization of the state and action spaces, namely, the Wasserstein distance between an underlying probability measure μ and a measure with finite support, and the Hausdorff distance between the original and the discretized actions sets. When approximating μ with its empirical probability measure we obtain convergence in probability at an exponential rate. An application to a queueing system is presented.< Réduire

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Continuous-time Markov decision process

Lipschitz continuous control model

Approximation of the optimal value function

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Computable approximations for average Markov decision processes in continuous time

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