We consider a class of $ {\Bbb R} ^d$-valued stochastic
control systems, with possibly unbounded costs. The systems
evolve according to a discrete-time equation
$x_{t+1}=G_n(x_t,a_t)+\xi _t$ ($t=0,1,\dots
$), for each fixed $n=0,1,\dots
, $ where the $\xi _t$ are i.i.d. random vectors, and
the $G_n$ are given functions converging pointwise to some
function $G_{\infty }$ as $n \to \infty $. Under suitable
hypotheses, our main results state the existence of stationary
control policies that are expected average
cost (EAC) optimal and sample path
average cost (SPAC) optimal for the
limiting control system $x_{t+1}=G_{\infty }(x_t,a_t)+\xi _t$
($t=0,1,\dots$).
Keywords:
consider class bbb d valued stochastic control systems possibly unbounded costs systems evolve according discrete time equation t dots each fixed dots where random vectors given functions converging pointwise function infty infty under suitable hypotheses main results state existence stationary control policies expected average cost eac optimal sample path average cost spac optimal limiting control system infty t dots
Affiliations des auteurs :
Nadine Hilgert
1
;
Onesimo Hernández-Lerma
2
1
Departamento de Matematicas CINVESTAV-IPN Apartado Postal 14-740 Mexico D.F. 07000, Mexico Permanent address Laboratoire de Biometrie INRA-ENSA.M 2 place Viala 34060 Montpellier Cedex 1, France
2
Departamento de Matematicas CINVESTAV-IPN Apartado Postal 14-740 Mexico D.F. 07000, Mexico
@article{10_4064_am28_1_8,
author = {Nadine Hilgert and Onesimo Hern\'andez-Lerma},
title = {Limiting average cost control problems
in a class of discrete-time stochastic systems},
journal = {Applicationes Mathematicae},
pages = {111--123},
year = {2001},
volume = {28},
number = {1},
doi = {10.4064/am28-1-8},
language = {en},
url = {http://geodesic.mathdoc.fr/articles/10.4064/am28-1-8/}
}
TY - JOUR
AU - Nadine Hilgert
AU - Onesimo Hernández-Lerma
TI - Limiting average cost control problems
in a class of discrete-time stochastic systems
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PY - 2001
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VL - 28
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%A Nadine Hilgert
%A Onesimo Hernández-Lerma
%T Limiting average cost control problems
in a class of discrete-time stochastic systems
%J Applicationes Mathematicae
%D 2001
%P 111-123
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Nadine Hilgert; Onesimo Hernández-Lerma. Limiting average cost control problems
in a class of discrete-time stochastic systems. Applicationes Mathematicae, Tome 28 (2001) no. 1, pp. 111-123. doi: 10.4064/am28-1-8
