Limiting average cost control problems in a class of discrete-time stochastic systems

Nadine Hilgert, and Onesimo Hernández-Lerma. "Limiting average cost control problems in a class of discrete-time stochastic systems." Applicationes Mathematicae 28.1 (2001): 111-123. <http://eudml.org/doc/279078>.

@article{NadineHilgert2001,
abstract = {We consider a class of $ℝ^d$-valued stochastic control systems, with possibly unbounded costs. The systems evolve according to a discrete-time equation $x_\{t+1\} = Gₙ(x_t,a_t)+ξ_t$ (t = 0,1,... ), for each fixed n = 0,1,..., where the $ξ_t$ are i.i.d. random vectors, and the Gₙ are given functions converging pointwise to some function $G_\{∞\}$ as n → ∞. 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 $x_\{t+1\} = G_\{∞\}(x_t,a_t)+ξ_t$ (t = 0,1,...).},
author = {Nadine Hilgert, Onesimo Hernández-Lerma},
journal = {Applicationes Mathematicae},
keywords = {nonhomogeneous Markov control processes; discrete-time stochastic systems; long-run average cost criteria; discounted cost; optimal policies; existence of stationary policies; unbounded costs},
language = {eng},
number = {1},
pages = {111-123},
title = {Limiting average cost control problems in a class of discrete-time stochastic systems},
url = {http://eudml.org/doc/279078},
volume = {28},
year = {2001},
}

TY - JOUR
AU - Nadine Hilgert
AU - Onesimo Hernández-Lerma
TI - Limiting average cost control problems in a class of discrete-time stochastic systems
JO - Applicationes Mathematicae
PY - 2001
VL - 28
IS - 1
SP - 111
EP - 123
AB - We consider a class of $ℝ^d$-valued stochastic control systems, with possibly unbounded costs. The systems evolve according to a discrete-time equation $x_{t+1} = Gₙ(x_t,a_t)+ξ_t$ (t = 0,1,... ), for each fixed n = 0,1,..., where the $ξ_t$ are i.i.d. random vectors, and the Gₙ are given functions converging pointwise to some function $G_{∞}$ as n → ∞. 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 $x_{t+1} = G_{∞}(x_t,a_t)+ξ_t$ (t = 0,1,...).
LA - eng
KW - nonhomogeneous Markov control processes; discrete-time stochastic systems; long-run average cost criteria; discounted cost; optimal policies; existence of stationary policies; unbounded costs
UR - http://eudml.org/doc/279078
ER -