A characterization of the optimal risk-sensitive average cost in finite controlled Markov chains

被引：29

作者：

Cavazos-Cadena, R ^{[1
]}

Hernández-Hernández, D

机构：

[1] Univ Autonoma Agraria Antonio Narro, Dept Estadist & Calculo, Saltillo 25315, Coahuila, Mexico

[2] Ctr Invest Matemat, Guanajuato 36000, GTO, Mexico

来源：

ANNALS OF APPLIED PROBABILITY | 2005年 / 15卷 / 1A期

关键词：

decreasing function along trajectories; stopping time; nearly optimal policies; Holder's inequality; simultaneous Doeblin condition; recurrent state;

D O I：

10.1214/105051604000000585

中图分类号：

O21 [概率论与数理统计]; C8 [统计学];

学科分类号：

020208 ; 070103 ; 0714 ;

摘要：

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.

引用

页码：175 / 212

页数：38

共 21 条

[11]

Dynkin E.B., 1979, Grundlehren der Mathematischen Wissenschaften, V235

[12]

Fleming WH, 1999, ANN APPL PROBAB, V9, P871

[13] Risk-sensitive control of finite state machines on an infinite horizon .1. [J].