The paper is devoted to properties of generalized set-valued stochastic integrals defined in [10]. These integrals generalize set-valued stochastic integrals defined by E.J. Jung and J.H. Kim in the paper [4]. Up to now we were not able to construct any example of set-valued stochastic processes, different on a singleton, having integrably bounded set-valued integrals defined in [4]. It was shown by M. Michta (see [11]) that in the general case set-valued stochastic integrals defined by E.J. Jung and J.H. Kim, are not integrably bounded. Generalized set-valued stochastic integrals, considered in the paper, are in some non-trivial cases square integrably bounded and can be applied in the theory of stochastic differential equations with set-valued solutions.
@article{bwmeta1.element.bwnjournal-article-doi-10_7151_dmdico_1155,
author = {Micha\l\ Kisielewicz},
title = {Properties of generalized set-valued stochastic integrals},
journal = {Discussiones Mathematicae, Differential Inclusions, Control and Optimization},
volume = {34},
year = {2014},
pages = {131-147},
zbl = {1329.60163},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_7151_dmdico_1155}
}
Michał Kisielewicz. Properties of generalized set-valued stochastic integrals. Discussiones Mathematicae, Differential Inclusions, Control and Optimization, Tome 34 (2014) pp. 131-147. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_7151_dmdico_1155/
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