Note on stability estimation in average Markov control processes
Jaime Martínez Sánchez; Elena Zaitseva
Kybernetika (2015)
- Volume: 51, Issue: 4, page 629-638
- ISSN: 0023-5954
Access Full Article
top
Abstract
topHow to cite
topMartínez Sánchez, Jaime, and Zaitseva, Elena. "Note on stability estimation in average Markov control processes." Kybernetika 51.4 (2015): 629-638. <http://eudml.org/doc/271798>.
@article{MartínezSánchez2015,
abstract = {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.},
author = {Martínez Sánchez, Jaime, Zaitseva, Elena},
journal = {Kybernetika},
keywords = {discrete-time Markov control processes; average criterion; stability index; Prokhorov metric},
language = {eng},
number = {4},
pages = {629-638},
publisher = {Institute of Information Theory and Automation AS CR},
title = {Note on stability estimation in average Markov control processes},
url = {http://eudml.org/doc/271798},
volume = {51},
year = {2015},
}
TY - JOUR
AU - Martínez Sánchez, Jaime
AU - Zaitseva, Elena
TI - Note on stability estimation in average Markov control processes
JO - Kybernetika
PY - 2015
PB - Institute of Information Theory and Automation AS CR
VL - 51
IS - 4
SP - 629
EP - 638
AB - 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.
LA - eng
KW - discrete-time Markov control processes; average criterion; stability index; Prokhorov metric
UR - http://eudml.org/doc/271798
ER -
References
top- Arapostathis, A., Borkar, V. S., Fernández-Gaucherand, E., Ghosh, M. K., Marcus, S. I., 10.1137/0331018, SIAM J. Control and Optimization 31 (1993), 282-344. Zbl0770.93064MR1205981DOI10.1137/0331018
- Dudley, R. M., 10.1017/s0013091500018265, Wadsworth and Brooks/Cole, Pacific Grove 1989. Zbl1023.60001MR0982264DOI10.1017/s0013091500018265
- Dudley, R. M., 10.1214/aoms/1177697802, Ann. Math. Stat. 40 (1969), 40-50. MR0236977DOI10.1214/aoms/1177697802
- Dynkin, E. B., Yushkevich, A. A., 10.1002/zamm.19810610317, Springer-Verlag, New York 1979. MR0554083DOI10.1002/zamm.19810610317
- Gordienko, E., Lemus-Rodríguez, E., Montes-de-Oca, R., 10.1007/s00186-008-0229-6, Math. Methods Oper. Res. 70 (2009), 13-33. Zbl1176.60062MR2529423DOI10.1007/s00186-008-0229-6
- Gordienko, E. I., 10.1007/bf01083641, J. Soviet. Math. 40 (1988), 481-486. Zbl0638.90101MR0957101DOI10.1007/bf01083641
- 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. Zbl1116.90401MR1990916
- Hernández-Lerma, O., 10.1007/978-1-4419-8714-3, Springer-Verlag, New York 1989. Zbl0677.93073MR0995463DOI10.1007/978-1-4419-8714-3
- 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. Zbl1249.90313MR2193864
- Rachev, S. T., Rüschendorf, L., Mass Transportation Problem, Vol. II: Applications., Springer, New York 1998. MR1619171
- Vega-Amaya, O., The average cost optimality equation: a fixed point approach., Bol. Soc. Math. Mexicana 9 (2003), 185-195. Zbl1176.90626MR1988598
NotesEmbed ?
topYou must be logged in to post comments.
To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.