Weak star convergence of martingales in a dual space

C. Castaing, et al. "Weak star convergence of martingales in a dual space." Banach Center Publications 92.1 (2011): 45-73. <http://eudml.org/doc/282564>.

@article{C2011,
abstract = {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.},
author = {C. Castaing, F. Ezzaki, M. Lavie, M. Saadoune},
journal = {Banach Center Publications},
keywords = {multivalued martingale; supermartingale; mil; weak star Kuratowski convergence; conditional expectation},
language = {eng},
number = {1},
pages = {45-73},
title = {Weak star convergence of martingales in a dual space},
url = {http://eudml.org/doc/282564},
volume = {92},
year = {2011},
}

TY - JOUR
AU - C. Castaing
AU - F. Ezzaki
AU - M. Lavie
AU - M. Saadoune
TI - Weak star convergence of martingales in a dual space
JO - Banach Center Publications
PY - 2011
VL - 92
IS - 1
SP - 45
EP - 73
AB - 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.
LA - eng
KW - multivalued martingale; supermartingale; mil; weak star Kuratowski convergence; conditional expectation
UR - http://eudml.org/doc/282564
ER -