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Markov jump processes; Feller process; inspections and maintenance; quasi-variational inequality; viscosity solutions
The paper deals with the optimal inspections and maintenance problem with costly information for a Markov process with positive discount factor. The associated dynamic programming equation is a quasi-variational inequality with first order differential terms. In this paper we study its different formulations: strong, visousity and evolutionary. The case of impulsive control of purely jump Markov processes is studied as a special case.
[1] R. F. Anderson A. Friedman: Optimal inspections in a stochastic control problem with costly observations. Math. Oper. Res. 2 (1977), 155-190. DOI 10.1287/moor.2.2.155 | MR 0479602
[2] G. Barles: Deterministic impulse control problems. SIAM Control Opt. 23 (1985), 419-432. DOI 10.1137/0323027 | MR 0784578 | Zbl 0571.49020
[3] A. Bensoussan J. L. Lions: Applications des Inequations Variationnelles en Controle Stochastique. Dunod, Paris 1978. MR 0513618
[4] M. H. A. Davis: Piecewise-deterministic Markov processes: a general class of non-diffusion Stochastic models. J. Royal Statist. Soc. (B), (46 (1984), 353 - 388. MR 0790622 | Zbl 0565.60070
[5] D. Gątarek: On value functions for impulsive control of piecewise-deterministic processes. to appear in Stochastics.
[6] D. Gątarek: Optimal maintenance and inspections of a decreasing Markov process. to appear in Mathematics of Operations Research.
[7] B. Hanouzet J. L. Joly: Convergence uniforme des iteres defmissant la solution d'une inequation quasi-variationelle abstaite. CRAS 286 (1978), 735-738. MR 0496035
[8] M. Robin: Controle Impulsionnel des Processus de Markov. Thesis, Université Paris IX, 1978.
[9] M. Robin: Optimal maintenance and inspections: am inpulsive control approach. Proc. 8 IFIP Symp. Opt. Lect. Notes Control Inf. Sc. 6, 1977, 186-198. MR 0529459
[10] Ł. Stettner J. Zabczyk: Optimal stopping for Feller processes. Institute of Mathematics PAS, Preprint 284, Warszawa 1983.
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