A martingale problem approach is used first to analyze compactness and continuous dependence of the solution set to stochastic differential inclusions of Ito type with convex integrands on the initial distributions. Next the problem of existence of optimal weak solutions to such inclusions and their dependence on the initial distributions is investigated.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-am29-4-2,
author = {Mariusz Michta},
title = {Optimal solutions to stochastic differential inclusions},
journal = {Applicationes Mathematicae},
volume = {29},
year = {2002},
pages = {387-398},
zbl = {1044.93062},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-am29-4-2}
}
Mariusz Michta. Optimal solutions to stochastic differential inclusions. Applicationes Mathematicae, Tome 29 (2002) pp. 387-398. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-am29-4-2/