Integrably bounded set-valued stochastic integrals

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• 作者：Michał Kisielewicz ; ^{M.Kisielewicz@wmie.uz.zgora.pl} ; Mariusz Michta ; ^{M.Michta@wmie.uz.zgora.pl}
• 关键词：Set-valued mapping ; Set-valued integral ; Set-valued stochastic process
• 刊名：Journal of Mathematical Analysis and Applications
• 出版年：2017
• 出版时间：15 May 2017
• 年：2017
• 卷：449
• 期：2
• 页码：1892-1910
• 全文大小：463 K
• 卷排序：449

文摘

The paper is devoted to properties of Aumann and Itô set-valued stochastic integrals, defined as some set-valued random variables. In particular the problem of integrable boundedness of the generalized Itô set-valued stochastic integrals is considered. Unfortunately, Itô set-valued stochastic integrals, defined by E.J. Jung and J.H. Kim in the paper [5], are not in general integrably bounded (see  and ). Therefore, in the present paper we consider generalized Itô set-valued stochastic integrals (see  and ) defined for absolutely summable and countable subsets of the space IL2(IR+×Ω,ΣIF,IRd×m) of all square integrable IF-nonanticipative matrix-valued stochastic processes. Such integrals are integrably bounded and possess properties needed in the theory of set-valued stochastic equations.