| Title:
|
Time-discretization for controlled Markov processes. I. General approximation results (English) |
| Author:
|
van Dijk, Nico M. |
| Author:
|
Hordijk, Arie |
| Language:
|
English |
| Journal:
|
Kybernetika |
| ISSN:
|
0023-5954 |
| Volume:
|
32 |
| Issue:
|
1 |
| Year:
|
1996 |
| Pages:
|
1-16 |
| . |
| Category:
|
math |
| . |
| MSC:
|
49K45 |
| MSC:
|
49M25 |
| MSC:
|
90C40 |
| MSC:
|
93C57 |
| MSC:
|
93E20 |
| idZBL:
|
Zbl 0874.93094 |
| idMR:
|
MR1380195 |
| . |
| Date available:
|
2009-09-24T19:00:07Z |
| Last updated:
|
2012-06-06 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/125234 |
| . |
| Related article:
|
http://dml.cz/handle/10338.dmlcz/124178 |
| . |
| Reference:
|
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| Reference:
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[2] N. Christopeit: Discrete approximation of continuous time stochastic control systems.SIAM J. Control Optim. 21 (1983), 1, 17-40. Zbl 0508.93065, MR 0688438 |
| Reference:
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[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. Zbl 0381.60086, MR 0499221 |
| Reference:
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[4] W. H. Fleming R. W. Rishel: Deterministic and Stochastic Optimal Control.Springer Verlag, Berlin 1975. MR 0454768 |
| Reference:
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[5] I. I. Gihman A. V. Skorohod: Controlled Stochastic Processes.Springer Verlag, Berlin 1979. MR 0544839 |
| Reference:
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[6] U. G. Haussmann: A discrete approximation to optimal stochastic.In: Analysis and Optimization of Stochastic Systems, Academic Press, London 1980, pp. 229-241. Zbl 0476.93082, MR 0592987 |
| Reference:
|
[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 0698820 |
| Reference:
|
[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 0736642 |
| Reference:
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[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 0787013 |
| Reference:
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[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 0859000 |
| Reference:
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[11] G. M. Koole: Stochastic Scheduling and Dynamic Programming.Ph.D. Thesis, University of Leiden 1992. |
| Reference:
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[12] T. G. Kurtz: Extensions of Trotter's operator semigroup approximations theorems.J. Funct. Anal. 3 (1969), 111-132. MR 0242016 |
| Reference:
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[13] H. J. Kushner: Probability Methods for Approximation in Stochastic Control and for Elliptic Equations.Academic Press, New York 1977. MR 0469468 |
| Reference:
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[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 0079204 |
| Reference:
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[15] T. Meis U. Marcowitz: Numerical Solution of Partial Differential Equations.Springer Verlag, Berlin 1981. MR 0617910 |
| Reference:
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[16] H. J. Plum: Impulsive and continuously acting control of jump processes -- Time discretization.Stochastics and Stochastic Reports 36 (1991), 163-192. Zbl 0739.60076, MR 1128492 |
| Reference:
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[17] R. Rishel: Necessary and sufficient dynamic programming conditions for continuous time stochastic optimal control.SIAM J. Control 8 (1970), 4, 559-571. Zbl 0206.45804, MR 0274161 |
| Reference:
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[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 0479611 |
| Reference:
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[19] F. A. Van der Duyn Schouten: Markov Decision Processes with Continuous Time Parameter.Mathematical Centre Tract 164, Amsterdam 1983. Zbl 0519.90052, MR 0709095 |
| Reference:
|
[20] N. M. Van Dijk: Controlled Markov Processes; Time Discretization/Networks of Queues.Ph.D. Thesis, University of Leiden 1983. |
| Reference:
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[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 0936380 |
| . |
