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Discounted cost optimality problem: Stability with respect to weak metrics. (English) Zbl 1166.60041
In the paper, inequalities to estimate the stability (robustness) of a discounted cost optimization problem for discrete-time Markov control processes are derived on a Borel state space. The one stage cost is allowed to be unbounded. Unlike the known results in this area we consider a perturbation of transition probabilities measured by the Kantorovich metric, closely related to the weak convergence. The results obtained make possible to estimate the vanishing rate of the stability index when approximation is made through empirical measures.

MSC:
60J05 Discrete-time Markov processes on general state spaces
60B05 Probability measures on topological spaces
93E15 Stochastic stability in control theory
93E20 Optimal stochastic control
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