Title:
|
Existence of average optimal policies in Markov control processes with strictly unbounded costs (English) |
Author:
|
Hernández-Lerma, Onésimo |
Language:
|
English |
Journal:
|
Kybernetika |
ISSN:
|
0023-5954 |
Volume:
|
29 |
Issue:
|
1 |
Year:
|
1993 |
Pages:
|
1-17 |
. |
Category:
|
math |
. |
MSC:
|
49L20 |
MSC:
|
90C40 |
MSC:
|
93E20 |
idZBL:
|
Zbl 0792.93120 |
idMR:
|
MR1227738 |
. |
Date available:
|
2009-09-24T18:37:59Z |
Last updated:
|
2012-06-06 |
Stable URL:
|
http://hdl.handle.net/10338.dmlcz/124548 |
. |
Reference:
|
[1] D. P. Bertsekas: Dynamic Programming: Deterministic and Stochastic Models.Prentice-Hall, Englewood Cliffs, N. J. 1987. Zbl 0649.93001, MR 0896902 |
Reference:
|
[2] D. P. Bertsekas, S. E. Shreve: Stochastic Optimal Control: The Discrete Time Case.Academic Press, New York 1978. Zbl 0471.93002, MR 0511544 |
Reference:
|
[3] P. Billingsley: Convergence of Probability Measures.Wiley, New York 1968. Zbl 0172.21201, MR 0233396 |
Reference:
|
[4] D. Blackwell: Memoryless strategies in finite-stage dynamic programming.Ann. Math. Statist. 35 (1964), 863-865. Zbl 0127.36406, MR 0162642 |
Reference:
|
[5] D. Blackwell: Discounted dynamic programming.Ann. Math. Statist. 36 (1965), 226-235. Zbl 0133.42805, MR 0173536 |
Reference:
|
[6] V. S. Borkar: Control of Markov chains with long-run average cost criterion: the dynamic programming equations.SIAM J. Control Optim. 27 (1989), 642-657. Zbl 0668.60059, MR 0993291 |
Reference:
|
[7] R. Cavazos-Cadena: Solution to the optimality equation in a class of average Markov decision chains with unbounded costs.Kybernetika 27 (1991), 23-37. MR 1099512 |
Reference:
|
[8] J. Diebolt, D. Guegan: Probabilistic properties of the general nonlinear markovian process of order one and applications to time series modelling.Rapport Technique No. 125, Laboratoire de Statistique Theorique et Appliquee, CNR-URA 1321, Universite Paris VI, 1990. |
Reference:
|
[9] J. L. Doob: Stochastic Processes.Wiley, New York 1953. Zbl 0053.26802, MR 0058896 |
Reference:
|
[10] M. Duflo: Methodes Recursives Aleatoires.Masson, Paris 1990. Zbl 0703.62084, MR 1082344 |
Reference:
|
[11] E. B. Dynkin, A. A. Yushkevich: Controlled Markov Processes.Springer - Verlag, Berlin 1979. MR 0554083 |
Reference:
|
[12] R. Hartley: Dynamic programming and an undiscounted, infinite horizon, convex stochastic control problem.In: Recent Developments in Markov Decision Processes (R. Hartley, L. C. Thomas and D.J. White, eds.). Academic Press, London 1980, pp. 277-300. |
Reference:
|
[13] O. Hernandez-Lerma: Lyapunov criteria for stability of differential equations with Markov parameters.Boletin Soc. Mat. Mexicana 24 (1979), 27-48. Zbl 0486.60051, MR 0579667 |
Reference:
|
[14] O. Hernandez-Lerma: Adaptive Markov Control Processes.Springer - Verlag, New York 1989. Zbl 0698.90053, MR 0995463 |
Reference:
|
[15] O. Hernandez-Lerma: Average optimality in dynamic programming on Borel spaces - unbounded costs and controls.Syst. Control Lett. 17 (1991), 237-242. Zbl 0771.90098, MR 1125975 |
Reference:
|
[16] O. Hernandez-Lerma, J. B. Lasserre: Average cost optimal policies for Markov control processes with Borel state space and unbounded costs.Syst. Control Lett. 15 (1990), 349-356. Zbl 0723.93080, MR 1078813 |
Reference:
|
[17] O. Hernandez-Lerma, J. B. Lasserre: Linear programming and average optimality of Markov control processes on Borel spaces - unbounded costs.Rapport LAAS, LAAS-CNRS, Toulouse 1992. To appear in SIAM J. Control Optim. MR 1261150 |
Reference:
|
[18] O. Hernandez-Lerma R. Montes de Oca, R. Cavazos-Cadena: Recurrence conditions for Markov decision processes with Borel state space: a survey.Ann. Oper. Res. 28 (1991), 29-46. MR 1105165 |
Reference:
|
[19] K. Hinderer: Foundations of Non-Stationary Dynamic Programming with Discrete Time Parameter.Springer-Verlag, Berlin 1970. Zbl 0202.18401, MR 0267890 |
Reference:
|
[20] M. Yu. Kitayev: Semi-Markov and jump Markov control models: average cost criterion.Theory Probab. Appl. 30 (1985), 272-288. MR 0792619 |
Reference:
|
[21] M. Kurano: The existence of a minimum pair of state and policy for Markov decision processes under the hypothesis of Doeblin.SIAM J. Control Optim. 27 (1989), 296-307. Zbl 0677.90085, MR 0984830 |
Reference:
|
[22] H. J. Kushner: Introduction to Stochastic Control.Holt, Rinehart and Winston, New York 1971. Zbl 0293.93018, MR 0280248 |
Reference:
|
[23] A. Leizarowitz: Optimal controls for diffusions in $R^n$.J. Math. Anal. Appl. 149 (1990), 180-209, MR 1054802 |
Reference:
|
[24] S. P. Meyn: Ergodic theorems for discrete time stochastic systems using a stochastic Lyapunov function.SIAM J. Control Optim. 27 (1989), 1409-1439. Zbl 0681.60067, MR 1022436 |
Reference:
|
[25] A. Mokkadem: Sur un modele autoregressif nonlineaire. Ergodicite et ergodicite geometrique.J. Time Series Anal. 8 (1987), 195-205. MR 0886138 |
Reference:
|
[26] D. Revuz: Markov Chains.Second edition. North-Holland, Amsterdam 1984. Zbl 0539.60073, MR 0758799 |
Reference:
|
[27] U. Rieder: Measurable selection theorems for optimization problems.Manuscripta Math. 24 (1978), 507-518. Zbl 0385.28005, MR 0493590 |
Reference:
|
[28] V. I. Rotar, T. A. Konyuhova: Two papers on asymptotic optimality in probability and almost surely.Preprint, Central Economic Mathematical Institute (CEMI), Moscow 1991. |
Reference:
|
[29] R. H. Stockbridge: Time-average control of martingale problems: a linear programming formulation.Ann. Probab. 18 (1990), 206-217. Zbl 0699.49019, MR 1043944 |
Reference:
|
[30] J. Wijngaard: Existence of average optimal strategies in markovian decision problems with strictly unbounded costs.In: Dynamic Programming and Its Applications (M. L. Puterman, ed.), Academic Press, New York 1978, pp. 369-386. Zbl 0458.90081, MR 0537889 |
Reference:
|
[31] K. Yosida: Functional Analysis.Fifth edition. Springer-Verlag, Berlin 1978. Zbl 0365.46001, MR 0500055 |
. |