Existence of average optimal policies in Markov control processes with strictly unbounded costs

 Access to full text

 Full (PDF)

1. D. P. Bertsekas, Dynamic Programming: Deterministic and Stochastic Models, Prentice-Hall, Englewood Cliffs, N. J. 1987. (1987) Zbl0649.93001MR0896902
2. D. P. Bertsekas, S. E. Shreve, Stochastic Optimal Control: The Discrete Time Case, Academic Press, New York 1978. (1978) Zbl0471.93002MR0511544
3. P. Billingsley, Convergence of Probability Measures, Wiley, New York 1968. (1968) Zbl0172.21201MR0233396
4. D. Blackwell, Memoryless strategies in finite-stage dynamic programming, Ann. Math. Statist. 35 (1964), 863-865. (1964) Zbl0127.36406MR0162642
5. D. Blackwell, Discounted dynamic programming, Ann. Math. Statist. 36 (1965), 226-235. (1965) Zbl0133.42805MR0173536
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. (1989) Zbl0668.60059MR0993291
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. (1991) MR1099512
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. (1990) 
9. J. L. Doob, Stochastic Processes, Wiley, New York 1953. (1953) Zbl0053.26802MR0058896
10. M. Duflo, Methodes Recursives Aleatoires, Masson, Paris 1990. (1990) Zbl0703.62084MR1082344
11. E. B. Dynkin, A. A. Yushkevich, Controlled Markov Processes, Springer - Verlag, Berlin 1979. (1979) MR0554083
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. (1980) 
13. O. Hernandez-Lerma, Lyapunov criteria for stability of differential equations with Markov parameters, Boletin Soc. Mat. Mexicana 24 (1979), 27-48. (1979) Zbl0486.60051MR0579667
14. O. Hernandez-Lerma, Adaptive Markov Control Processes, Springer - Verlag, New York 1989. (1989) Zbl0698.90053MR0995463
15. O. Hernandez-Lerma, Average optimality in dynamic programming on Borel spaces - unbounded costs and controls, Syst. Control Lett. 17 (1991), 237-242. (1991) Zbl0771.90098MR1125975
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. (1990) Zbl0723.93080MR1078813
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. (1992) MR1261150
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. (1991) MR1105165
19. K. Hinderer, Foundations of Non-Stationary Dynamic Programming with Discrete Time Parameter, Springer-Verlag, Berlin 1970. (1970) Zbl0202.18401MR0267890
20. M. Yu. Kitayev, Semi-Markov and jump Markov control models: average cost criterion, Theory Probab. Appl. 30 (1985), 272-288. (1985) MR0792619
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. (1989) Zbl0677.90085MR0984830
22. H. J. Kushner, Introduction to Stochastic Control, Holt, Rinehart and Winston, New York 1971. (1971) Zbl0293.93018MR0280248
23. A. Leizarowitz, Optimal controls for diffusions in $R^n$, J. Math. Anal. Appl. 149 (1990), 180-209, (1990) MR1054802
24. S. P. Meyn, Ergodic theorems for discrete time stochastic systems using a stochastic Lyapunov function, SIAM J. Control Optim. 27 (1989), 1409-1439. (1989) Zbl0681.60067MR1022436
25. A. Mokkadem, Sur un modele autoregressif nonlineaire. Ergodicite et ergodicite geometrique, J. Time Series Anal. 8 (1987), 195-205. (1987) MR0886138
26. D. Revuz, Markov Chains, Second edition. North-Holland, Amsterdam 1984. (1984) Zbl0539.60073MR0758799
27. U. Rieder, Measurable selection theorems for optimization problems, Manuscripta Math. 24 (1978), 507-518. (1978) Zbl0385.28005MR0493590
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. (1991) 
29. R. H. Stockbridge, Time-average control of martingale problems: a linear programming formulation, Ann. Probab. 18 (1990), 206-217. (1990) Zbl0699.49019MR1043944
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. (1978) Zbl0458.90081MR0537889
31. K. Yosida, Functional Analysis, Fifth edition. Springer-Verlag, Berlin 1978. (1978) Zbl0365.46001MR0500055

1. Daniel Hernández-Hernández, Onésimo Hernández-Lerma, Michael Taksar, The linear programming approach to deterministic optimal control problems
2. Oscar Vega-Amaya, Sample path average optimality of Markov control processes with strictly unbounded cost