We define the notion of a Markov strategy for the general optimal control problem where the index set is partially ordered. We prove that the supremum over all strategies is always attained by a Markov strategy if and only if the structure of the probability space is that of a Markov random field.
Publié le : 1983-08-14
Classification:
Optimal control problem,
partially ordered index set,
Markov strategies,
60G40,
60G45
@article{1176993508,
author = {Lawler, G. F. and Vanderbei, R. J.},
title = {Markov Strategies for Optimal Control Problems Indexed by a Partially Ordered Set},
journal = {Ann. Probab.},
volume = {11},
number = {4},
year = {1983},
pages = { 642-647},
language = {en},
url = {http://dml.mathdoc.fr/item/1176993508}
}
Lawler, G. F.; Vanderbei, R. J. Markov Strategies for Optimal Control Problems Indexed by a Partially Ordered Set. Ann. Probab., Tome 11 (1983) no. 4, pp. 642-647. http://gdmltest.u-ga.fr/item/1176993508/