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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.

Reviewer: Pavel Gapeev (London)

### 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 |

### Keywords:

discrete-time Markov control process; total discounted cost; stability inequalities; Kantorovich metric; empirical measure
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\textit{E. Gordienko} et al., Math. Methods Oper. Res. 68, No. 1, 77--96 (2008; Zbl 1166.60041)

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