In this paper we present various weak star Kuratowski convergence results for multivalued martingales, supermartingales and multivalued mils in the dual of a separable Banach space. We establish several integral representation formulas for convex weak star compact valued multifunctions defined on a Köthe space and derive several existence results of conditional expectation for multivalued Gelfand-integrable multifunctions. Similar convergence results for Gelfand-integrable martingales in the dual space are provided. We also present a new version of Mosco convergence result for unbounded closed convex integrable supermartingales in a separable Banach spaces having the Radon-Nikodym property. New application to the law of large numbers is also presented.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-bc92-0-4,
author = {C. Castaing and F. Ezzaki and M. Lavie and M. Saadoune},
title = {Weak star convergence of martingales in a dual space},
journal = {Banach Center Publications},
volume = {95},
year = {2011},
pages = {45-73},
zbl = {1238.28011},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-bc92-0-4}
}
C. Castaing; F. Ezzaki; M. Lavie; M. Saadoune. Weak star convergence of martingales in a dual space. Banach Center Publications, Tome 95 (2011) pp. 45-73. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-bc92-0-4/