| Title:
|
Note on stability estimation in average Markov control processes (English) |
| Author:
|
Martínez Sánchez, Jaime |
| Author:
|
Zaitseva, Elena |
| Language:
|
English |
| Journal:
|
Kybernetika |
| ISSN:
|
0023-5954 (print) |
| ISSN:
|
1805-949X (online) |
| Volume:
|
51 |
| Issue:
|
4 |
| Year:
|
2015 |
| Pages:
|
629-638 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
We study the stability of average optimal control of general discrete-time Markov processes. Under certain ergodicity and Lipschitz conditions the stability index is bounded by a constant times the Prokhorov distance between distributions of random vectors determinating the “original and the perturbated” control processes. (English) |
| Keyword:
|
discrete-time Markov control processes |
| Keyword:
|
average criterion |
| Keyword:
|
stability index |
| Keyword:
|
Prokhorov metric |
| MSC:
|
90C40 |
| MSC:
|
93E20 |
| idZBL:
|
Zbl 06537775 |
| idMR:
|
MR3423190 |
| DOI:
|
10.14736/kyb-2015-4-0629 |
| . |
| Date available:
|
2015-11-20T12:16:52Z |
| Last updated:
|
2016-04-02 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/144471 |
| . |
| Reference:
|
[1] Arapostathis, A., Borkar, V. S., Fernández-Gaucherand, E., Ghosh, M. K., Marcus, S. I.: Discrete-time controlled Markov processes with average cost criterion: A survey..SIAM J. Control and Optimization 31 (1993), 282-344. Zbl 0770.93064, MR 1205981, 10.1137/0331018 |
| Reference:
|
[2] Dudley, R. M.: Real Analysis and Probability..Wadsworth and Brooks/Cole, Pacific Grove 1989. Zbl 1023.60001, MR 0982264, 10.1017/s0013091500018265 |
| Reference:
|
[3] Dudley, R. M.: The speed of mean Glivenko-Cantelly convergence..Ann. Math. Stat. 40 (1969), 40-50. MR 0236977, 10.1214/aoms/1177697802 |
| Reference:
|
[4] Dynkin, E. B., Yushkevich, A. A.: Controlled Markov Processes..Springer-Verlag, New York 1979. MR 0554083, 10.1002/zamm.19810610317 |
| Reference:
|
[5] Gordienko, E., Lemus-Rodríguez, E., Montes-de-Oca, R.: Average cost Markov control processes: stability with respect to the Kantorovich metric..Math. Methods Oper. Res. 70 (2009), 13-33. Zbl 1176.60062, MR 2529423, 10.1007/s00186-008-0229-6 |
| Reference:
|
[6] Gordienko, E. I.: Stability estimates for controlled Markov chains with a minorant..J. Soviet. Math. 40 (1988), 481-486. Zbl 0638.90101, MR 0957101, 10.1007/bf01083641 |
| Reference:
|
[7] Gordienko, E. I., Yushkevich, A. A.: Stability estimates in the problem of average optimal switching of a Markov Chain..Math. Methods Oper. Res. 57 (2003), 345-365. Zbl 1116.90401, MR 1990916 |
| Reference:
|
[8] Hernández-Lerma, O.: Adaptive Markov Control Processes..Springer-Verlag, New York 1989. Zbl 0677.93073, MR 0995463, 10.1007/978-1-4419-8714-3 |
| Reference:
|
[9] Montes-de-Oca, R., Salem-Silva, F.: Estimates for perturbations of average Markov decision processes with a minimal state and upper bounded by stochastically ordered Markov chains..Kybernetika 41 (2005), 757-772. Zbl 1249.90313, MR 2193864 |
| Reference:
|
[10] Rachev, S. T., Rüschendorf, L.: Mass Transportation Problem, Vol. II: Applications..Springer, New York 1998. MR 1619171 |
| Reference:
|
[11] Vega-Amaya, O.: The average cost optimality equation: a fixed point approach..Bol. Soc. Math. Mexicana 9 (2003), 185-195. Zbl 1176.90626, MR 1988598 |
| . |
