Geodesic
Asymptotic properties and optimization of some non-Markovian stochastic processes
Kybernetika, Tome 45 (2009) no. 3, pp. 475-490 Cet article a éte moissonné depuis la source Czech Digital Mathematics Library

Voir la notice de l'article

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.
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.
Classification : 60F15, 62M09, 90B05, 90C40, 93C55, 93E20
Keywords: nonmarkovian control sequence; average cost; attracting point; nonlinear optimitation; stability 
@article{KYB_2009_45_3_a7,
     author = {Gordienko, Evgueni and Garcia, Antonio and Chavez, Juan Ruiz de},
     title = {Asymptotic properties and optimization of some {non-Markovian} stochastic processes},
     journal = {Kybernetika},
     pages = {475--490},
     year = {2009},
     volume = {45},
     number = {3},
     mrnumber = {2543135},
     zbl = {1165.62333},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/KYB_2009_45_3_a7/}
}
TY  - JOUR
AU  - Gordienko, Evgueni
AU  - Garcia, Antonio
AU  - Chavez, Juan Ruiz de
TI  - Asymptotic properties and optimization of some non-Markovian stochastic processes
JO  - Kybernetika
PY  - 2009
SP  - 475
EP  - 490
VL  - 45
IS  - 3
UR  - http://geodesic.mathdoc.fr/item/KYB_2009_45_3_a7/
LA  - en
ID  - KYB_2009_45_3_a7
ER  - 
%0 Journal Article
%A Gordienko, Evgueni
%A Garcia, Antonio
%A Chavez, Juan Ruiz de
%T Asymptotic properties and optimization of some non-Markovian stochastic processes
%J Kybernetika
%D 2009
%P 475-490
%V 45
%N 3
%U http://geodesic.mathdoc.fr/item/KYB_2009_45_3_a7/
%G en
%F KYB_2009_45_3_a7
Gordienko, Evgueni; Garcia, Antonio; Chavez, Juan Ruiz de. Asymptotic properties and optimization of some non-Markovian stochastic processes. Kybernetika, Tome 45 (2009) no. 3, pp. 475-490. http://geodesic.mathdoc.fr/item/KYB_2009_45_3_a7/

[1] M. Duflo: Random Iterative Models. Springer-Verlag, Berlin 1997. | MR | Zbl

[2] E. B. Dynkin and A. A. Yushkevich: Controlled Markov Processes. Springer-Verlag, New York 1979. | MR

[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

[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

[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

[6] O. Hernández-Lerma and J. B. Lasserre: Discrete-Time Markov Control Processes. Springer-Verlag, New York 1996. | MR

[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

[8] E. L. Porteus: Foundations of Stochastic Inventory Theory. Stanford University Press, Stanford 2002.

[9] S. T. Rachev and L. Rüschendorf: Mass Transportation Problems. Vol. II. Springer-Verlag, New York 1998. | MR

[10] T. N. Saadawi, M. H. Ammar and A. El Hakeen: Fundamentals of Telecomunication Networks. Wiley, New York 1994.

[11] V. G. Sragovich: Mathematical Theory of Adaptive Control. World Scientific, New Jersey 2006. | MR