The first exit of almost strongly recurrent semi-Markov processes

Joachim Domsta; Franciszek Grabski

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We offer the quantitative estimation of stability of risk-sensitive cost optimization in the problem of optimal stopping of Markov chain on a Borel space $X$ . It is supposed that the transition probability $p (\cdot | x)$ , $x \in X$ is approximated by the transition probability $\tilde{p} (\cdot | x)$ , $x \in X$ , and that the stopping rule ${\tilde{f}}_{*}$ , which is optimal for the process with the transition probability $\tilde{p}$ is applied to the process with the transition probability $p$ . We give an upper bound (expressed in term of the total variation distance:...

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