## Approximation, estimation and control of stochastic systems under a randomized discounted cost criterion.(English)Zbl 1190.93105

Summary: 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 $$\alpha_t$$ evolve according to the coupled difference equations $$x_{t+1}= F(x_t\alpha_t,a_t,\xi_t)$$, $$\alpha_{t+1}= G(\alpha_t,\eta_t)$$ where the state and discount disturbance processes $$\xi_t$$ and $$\eta_t$$ are sequences of i.i.d. random variables with densities $$\rho^\xi$$ and $$\rho^\eta$$ respectively. The main objective is to introduce approximation algorithms of the optimal cost function that lead up to construction of optimal or nearly optimal policies in the cases when the densities $$\rho^\xi$$ and $$\rho^\eta$$ are either known or unknown. In the latter case, we combine suitable estimation methods with control procedures to construct an asymptotically discounted optimal policy.

### MSC:

 93E20 Optimal stochastic control 90C40 Markov and semi-Markov decision processes 93E10 Estimation and detection in stochastic control theory 93C55 Discrete-time control/observation systems
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### References:

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