This work concerns controlled Markov chains with finite state and action spaces. The transition law satisfies the simultaneous Doeblin condition, and the performance of a control policy is measured by the (long-run) risk-sensitive average cost criterion associated to a positive, but otherwise arbitrary, risk sensitivity coefficient. Within this context, the optimal risk-sensitive average cost is characterized via a minimization problem in a finite-dimensional Euclidean space.
Publié le : 2005-02-14
Classification:
Decreasing function along trajectories,
stopping time,
nearly optimal policies,
Hölder’s inequality,
simultaneous Doeblin condition,
recurrent state,
93E20,
60F10,
93C55
@article{1106922326,
author = {Cavazos-Cadena, Rolando and Hern\'andez-Hern\'andez, Daniel},
title = {A characterization of the optimal risk-sensitive average cost in finite controlled Markov chains},
journal = {Ann. Appl. Probab.},
volume = {15},
number = {1A},
year = {2005},
pages = { 175-212},
language = {en},
url = {http://dml.mathdoc.fr/item/1106922326}
}
Cavazos-Cadena, Rolando; Hernández-Hernández, Daniel. A characterization of the optimal risk-sensitive average cost in finite controlled Markov chains. Ann. Appl. Probab., Tome 15 (2005) no. 1A, pp. 175-212. http://gdmltest.u-ga.fr/item/1106922326/