| Abstrakt: |
Abstract: In this paper we are concerned with a class of time-varying discounted Markov decision models Mn with unbounded costs cn and state-action dependent discount factors. Specifically we study controlled systems whose state process evolves according to the equation xn+1=Gn(xn, n=0,1,..., with state-action dependent discount factors of the form αn(xn, an), where an and ξn are the control and the random disturbance at time n, respectively. Assuming that the sequences of functions {αn},{cn} and {Gn} converge, in certain sense, to α∞, c∞ and G∞, our objective is to introduce a suitable control model for this class of systems and then, to show the existence of optimal policies for the limit system M∞ corresponding to α∞, c∞ and G∞. Finally, we illustrate our results and their applicability in a class of semi-Markov control models. |
