Geodesic
Time-discretization for controlled Markov processes. I. General approximation results
Kybernetika, Tome 32 (1996) no. 1, pp. 1-16 Cet article a éte moissonné depuis la source Czech Digital Mathematics Library

Voir la notice de l'article

Classification : 49K45, 49M25, 90C40, 93C57, 93E20 
@article{KYB_1996_32_1_a0,
     author = {van Dijk, Nico M. and Hordijk, Arie},
     title = {Time-discretization for controlled {Markov} processes. {I.} {General} approximation results},
     journal = {Kybernetika},
     pages = {1--16},
     year = {1996},
     volume = {32},
     number = {1},
     mrnumber = {1380195},
     zbl = {0874.93094},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/KYB_1996_32_1_a0/}
}
TY  - JOUR
AU  - van Dijk, Nico M.
AU  - Hordijk, Arie
TI  - Time-discretization for controlled Markov processes. I. General approximation results
JO  - Kybernetika
PY  - 1996
SP  - 1
EP  - 16
VL  - 32
IS  - 1
UR  - http://geodesic.mathdoc.fr/item/KYB_1996_32_1_a0/
LA  - en
ID  - KYB_1996_32_1_a0
ER  - 
%0 Journal Article
%A van Dijk, Nico M.
%A Hordijk, Arie
%T Time-discretization for controlled Markov processes. I. General approximation results
%J Kybernetika
%D 1996
%P 1-16
%V 32
%N 1
%U http://geodesic.mathdoc.fr/item/KYB_1996_32_1_a0/
%G en
%F KYB_1996_32_1_a0
van Dijk, Nico M.; Hordijk, Arie. Time-discretization for controlled Markov processes. I. General approximation results. Kybernetika, Tome 32 (1996) no. 1, pp. 1-16. http://geodesic.mathdoc.fr/item/KYB_1996_32_1_a0/

[1] A. Bensoussan M. Robin: On the convergence of the discrete time dynamic programming equation for general semi-groups. SIAM J. Control Optim. 20 (1982), 1, 722-746. | MR

[2] N. Christopeit: Discrete approximation of continuous time stochastic control systems. SIAM J. Control Optim. 21 (1983), 1, 17-40. | MR | Zbl

[3] B. T. Doshi: Optimal control of the service rate in an $M|G|1$-queueing system. Adv. in Appl. Probab. 10 (1978), 682-701. | MR | Zbl

[4] W. H. Fleming R. W. Rishel: Deterministic and Stochastic Optimal Control. Springer Verlag, Berlin 1975. | MR

[5] I. I. Gihman A. V. Skorohod: Controlled Stochastic Processes. Springer Verlag, Berlin 1979. | MR

[6] U. G. Haussmann: A discrete approximation to optimal stochastic. In: Analysis and Optimization of Stochastic Systems, Academic Press, London 1980, pp. 229-241. | MR | Zbl

[7] A. Hordijk F. A. Van der Duyn Schouten: Average optimal policies in Markov decision drift processes with applications to queueing and replacement model. Adv. in Appl. Probab. 15 (1983), 274-303. | MR

[8] A. Hordijk F. A. Van der Duyn Schouten: Discretization and weak convergence in Markov decision drift processes. Math. Oper. Res. 9 (1984), 1, 112-141. | MR

[9] A. Hordijk F. A. Van der Duyn Schouten: Markov decision drift processes; Conditions for optimality obtained by discretization. Math. Oper. Res. 10 (1985), 160-173. | MR

[10] A. Hordijk F. A. Van der Duyn Schouten: On the optimality of $(s,S)$-policies in continuous review inventory models. SIAM J. Appl. Math. 46 (1986), 912-929. | MR

[11] G. M. Koole: Stochastic Scheduling and Dynamic Programming. Ph.D. Thesis, University of Leiden 1992.

[12] T. G. Kurtz: Extensions of Trotter's operator semigroup approximations theorems. J. Funct. Anal. 3 (1969), 111-132. | MR

[13] H. J. Kushner: Probability Methods for Approximation in Stochastic Control and for Elliptic Equations. Academic Press, New York 1977. | MR

[14] P. D. Lax R. D. Richtmeyer: Survey of the stability of linear finite difference equations. Comm. Pure Appl. Math. 9 (1956), 267-293. | MR

[15] T. Meis U. Marcowitz: Numerical Solution of Partial Differential Equations. Springer Verlag, Berlin 1981. | MR

[16] H. J. Plum: Impulsive and continuously acting control of jump processes -- Time discretization. Stochastics and Stochastic Reports 36 (1991), 163-192. | MR | Zbl

[17] R. Rishel: Necessary and sufficient dynamic programming conditions for continuous time stochastic optimal control. SIAM J. Control 8 (1970), 4, 559-571. | MR | Zbl

[18] R. Rishel: Controls optimal from the toward and dynamic programming for systems of controlled jump processes. Math. Programming Study 6 (1976), 125-153. | MR

[19] F. A. Van der Duyn Schouten: Markov Decision Processes with Continuous Time Parameter. Mathematical Centre Tract 164, Amsterdam 1983. | MR | Zbl

[20] N. M. Van Dijk: Controlled Markov Processes; Time Discretization/Networks of Queues. Ph.D. Thesis, University of Leiden 1983.

[21] N. M. Van Dijk: On the finite horizon Bellman equation for controlled Markov jump models with unbounded characteristics: existence and approximations. Stochastic Process. Appl. 28 (1988), 141-157. | MR