## Abstract

The paper deals with a class of discrete-time stochastic control processes under a discounted optimality criterion with random discount rate, and possibly unbounded costs. The state process {x _{t}} and the discount process {a _{t};} evolve according to the coupled difference equations x _{t/+}i = F(x _{t},a _{t}t,a _{t}ξ _{t}), a _{t+1} = G(a _{t},n _{t}) where the state and discount disturbance processes {ξ _{t}} and {η _{t}} are sequences of i.i.d. random variables with unknown distributions θξ and θ ^{η}" respectively. Assuming observability of the process {(St, ξ _{t})), we use the empirical estimator of its distribution to construct asymptotically discounted optimal policie.

Original language | English |
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Pages (from-to) | 149-163 |

Number of pages | 15 |

Journal | Boletin de la Sociedad Matematica Mexicana |

Volume | 14 |

Issue number | 1 |

State | Published - Apr 2008 |

## Keywords

- Discounted cost criterion
- Discrete-time stochastic systems
- Empirical distribution
- Optimal adaptive policy
- Random rate