# Bibliography

Journal Article

### Sample-Path Optimal Stationary Policies in Stable Markov Decision Chains with Average Reward Criterion

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**: **Journal of Applied Probability vol.52, 2 (2015), p. 419-440

**: **171396, GA AV ČR

**: **Dominated Convergence theorem for the expected average criterion,
Discrepancy function,
Kolmogorov inequality,
Innovations,
Strong sample-path optimality

**: **http://library.utia.cas.cz/separaty/2015/E/sladky-0449029.pdf

**(eng): **This work concerns discrete-time Markov decision chains with denumerable state and compact action sets. Besides standard continuity requirements, the main assumption on the model is that it admits a Lyapunov function m. In this context the average reward criterion is analyzed from the sample-path point of view. The main conclusion is that, if the expected average reward associated to m^2 is finite under any policy, then a stationary policy obtained from the optimality equation in the standard way is sample-path average optimal in a strong sense.

**: **BC