| Title:
|
Asymptotic properties and optimization of some non-Markovian stochastic processes (English) |
| Author:
|
Gordienko, Evgueni |
| Author:
|
Garcia, Antonio |
| Author:
|
Chavez, Juan Ruiz de |
| Language:
|
English |
| Journal:
|
Kybernetika |
| ISSN:
|
0023-5954 |
| Volume:
|
45 |
| Issue:
|
3 |
| Year:
|
2009 |
| Pages:
|
475-490 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
We study the limit behavior of certain classes of dependent random sequences (processes) which do not possess the Markov property. Assuming these processes depend on a control parameter we show that the optimization of the control can be reduced to a problem of nonlinear optimization. Under certain hypotheses we establish the stability of such optimization problems. (English) |
| Keyword:
|
nonmarkovian control sequence |
| Keyword:
|
average cost |
| Keyword:
|
attracting point |
| Keyword:
|
nonlinear optimitation |
| Keyword:
|
stability |
| MSC:
|
60F15 |
| MSC:
|
62M09 |
| MSC:
|
90B05 |
| MSC:
|
90C40 |
| MSC:
|
93C55 |
| MSC:
|
93E20 |
| idZBL:
|
Zbl 1165.62333 |
| idMR:
|
MR2543135 |
| . |
| Date available:
|
2010-06-02T18:44:54Z |
| Last updated:
|
2012-06-06 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/140019 |
| . |
| Reference:
|
[1] M. Duflo: Random Iterative Models.Springer-Verlag, Berlin 1997. Zbl 0868.62069, MR 1485774 |
| Reference:
|
[2] E. B. Dynkin and A. A. Yushkevich: Controlled Markov Processes.Springer-Verlag, New York 1979. MR 0554083 |
| Reference:
|
[3] E. I. Gordienko: An estimate of the stability of optimal control of certain stochastic and deterministic systems.J. Soviet Math. 50 (1992), 891–899. (Translated from the Russian publication of 1989). MR 1163393 |
| Reference:
|
[4] E. I. Gordienko and A. A. Yushkevich: Stability estimates in the problem of average optimal switching of a Markov chain.Math. Methods Oper. Res. 57 (2003), 345–365. MR 1990916 |
| Reference:
|
[5] X. Guo and Q. Zhu: Average optimality for Markov decision processes in Borel spaces: a new condition and approach.J. Appl. Probab. 43 (2006), 318–334. MR 2248567 |
| Reference:
|
[6] O. Hernández-Lerma and J. B. Lasserre: Discrete-Time Markov Control Processes.Springer-Verlag, New York 1996. MR 1363487 |
| Reference:
|
[7] R. Montes-de-Oca and F. Salem-Silva: Estimates for perturbations and average Markov decision processes with a minimal state and upper bounded by stochastically ordered Markov chains.Kybernetika 41 (2005), 757–772. MR 2193864 |
| Reference:
|
[8] E. L. Porteus: Foundations of Stochastic Inventory Theory.Stanford University Press, Stanford 2002. |
| Reference:
|
[9] S. T. Rachev and L. Rüschendorf: Mass Transportation Problems.Vol. II. Springer-Verlag, New York 1998. MR 1619171 |
| Reference:
|
[10] T. N. Saadawi, M. H. Ammar and A. El Hakeen: Fundamentals of Telecomunication Networks.Wiley, New York 1994. |
| Reference:
|
[11] V. G. Sragovich: Mathematical Theory of Adaptive Control.World Scientific, New Jersey 2006. MR 2206045 |
| . |
