Geodesic
Estimates of stability of Markov control processes with unbounded costs
Kybernetika, Tome 36 (2000) no. 2, p. [195]

Voir la notice de l'article provenant de la source Czech Digital Mathematics Library

For a discrete-time Markov control process with the transition probability $p$, we compare the total discounted costs $V_\beta $ $(\pi _\beta )$ and $V_\beta (\tilde{\pi }_\beta )$, when applying the optimal control policy $\pi _\beta $ and its approximation $\tilde{\pi }_\beta $. The policy $\tilde{\pi }_\beta $ is optimal for an approximating process with the transition probability $\tilde{p}$. A cost per stage for considered processes can be unbounded. Under certain ergodicity assumptions we establish the upper bound for the relative stability index $[V_\beta (\tilde{\pi }_\beta )-V_\beta (\pi _\beta )]/V_\beta (\pi _\beta )$. This bound does not depend on a discount factor $\beta \in (0,1)$ and this is given in terms of the total variation distance between $p$ and $\tilde{p}$.
Classification : 60J99, 90C40, 93C55, 93E20
Keywords: discrete-time Markov control process; unbounded cost 
@article{KYB_2000__36_2_a3,
     author = {Gordienko, Evgueni I. and Salem, Francisco},
     title = {Estimates of stability of {Markov} control processes with unbounded costs},
     journal = {Kybernetika},
     pages = {[195]},
     publisher = {mathdoc},
     volume = {36},
     number = {2},
     year = {2000},
     mrnumber = {1760024},
     zbl = {1249.93176},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/KYB_2000__36_2_a3/}
}
TY  - JOUR
AU  - Gordienko, Evgueni I.
AU  - Salem, Francisco
TI  - Estimates of stability of Markov control processes with unbounded costs
JO  - Kybernetika
PY  - 2000
SP  - [195]
VL  - 36
IS  - 2
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/KYB_2000__36_2_a3/
LA  - en
ID  - KYB_2000__36_2_a3
ER  - 
%0 Journal Article
%A Gordienko, Evgueni I.
%A Salem, Francisco
%T Estimates of stability of Markov control processes with unbounded costs
%J Kybernetika
%D 2000
%P [195]
%V 36
%N 2
%I mathdoc
%U http://geodesic.mathdoc.fr/item/KYB_2000__36_2_a3/
%G en
%F KYB_2000__36_2_a3
Gordienko, Evgueni I.; Salem, Francisco. Estimates of stability of Markov control processes with unbounded costs. Kybernetika, Tome 36 (2000) no. 2, p. [195]. http://geodesic.mathdoc.fr/item/KYB_2000__36_2_a3/