| Title:
|
A note on impulsive control of Feller processes with costly information (English) |
| Author:
|
Gątarek, Dariusz |
| Language:
|
English |
| Journal:
|
Aplikace matematiky |
| ISSN:
|
0373-6725 |
| Volume:
|
35 |
| Issue:
|
1 |
| Year:
|
1990 |
| Pages:
|
51-59 |
| . |
| Category:
|
math |
| . |
| Summary:
|
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. (English) |
| Keyword:
|
Markov jump processes |
| Keyword:
|
Feller process |
| Keyword:
|
inspections and maintenance |
| Keyword:
|
quasi-variational inequality |
| Keyword:
|
viscosity solutions |
| MSC:
|
60G35 |
| MSC:
|
60J75 |
| MSC:
|
60J99 |
| MSC:
|
90B25 |
| MSC:
|
93C57 |
| idZBL:
|
Zbl 0699.60032 |
| idMR:
|
MR1039410 |
| DOI:
|
10.21136/AM.1990.104386 |
| . |
| Date available:
|
2008-05-20T18:38:21Z |
| Last updated:
|
2020-07-28 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/104386 |
| . |
| Reference:
|
[1] R. F. Anderson A. Friedman: Optimal inspections in a stochastic control problem with costly observations.Math. Oper. Res. 2 (1977), 155-190. MR 0479602, 10.1287/moor.2.2.155 |
| Reference:
|
[2] G. Barles: Deterministic impulse control problems.SIAM Control Opt. 23 (1985), 419-432. Zbl 0571.49020, MR 0784578, 10.1137/0323027 |
| Reference:
|
[3] A. Bensoussan J. L. Lions: Applications des Inequations Variationnelles en Controle Stochastique.Dunod, Paris 1978. MR 0513618 |
| Reference:
|
[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. Zbl 0565.60070, MR 0790622 |
| Reference:
|
[5] D. Gątarek: On value functions for impulsive control of piecewise-deterministic processes.to appear in Stochastics. |
| Reference:
|
[6] D. Gątarek: Optimal maintenance and inspections of a decreasing Markov process.to appear in Mathematics of Operations Research. |
| Reference:
|
[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 |
| Reference:
|
[8] M. Robin: Controle Impulsionnel des Processus de Markov.Thesis, Université Paris IX, 1978. |
| Reference:
|
[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 |
| Reference:
|
[10] Ł. Stettner J. Zabczyk: Optimal stopping for Feller processes.Institute of Mathematics PAS, Preprint 284, Warszawa 1983. |
| . |
