A+ CATEGORY SCIENTIFIC UNIT

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

Volume 28 / 2001

Nadine Hilgert, Onesimo Hernández-Lerma Applicationes Mathematicae 28 (2001), 111-123 MSC: 93E20, 90C40. DOI: 10.4064/am28-1-8

Abstract

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 $x_{t+1}=G_{\infty }(x_t,a_t)+\xi _t$ ($t=0,1,\dots$).

Authors

  • Nadine HilgertDepartamento 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
    e-mail
  • Onesimo Hernández-LermaDepartamento de Matematicas
    CINVESTAV-IPN
    Apartado Postal 14-740
    Mexico D.F. 07000, Mexico
    e-mail

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