Selection theorems for set-valued stochastic integrals. Issue 2 (4th March 2019)

• Record Type: Journal Article
• Authors: Kisielewicz, Michał; Motyl, Jerzy
• Is Part Of: Stochastic analysis and applications. Volume 37:Issue 2(2019)
• Page Start: 243
• Page End: 270
• Publication Date: 2019-03-04
• Subjects: Set-valued mappings -- set-valued integrals -- set-valued stochastic processes -- decomposable sets; 60H05 -- 28B20 -- 47H04; Stochastic analysis -- Periodicals; 519.2205
• DOI: 10.1080/07362994.2018.1551142
• Languages: English
• ISSNs: 0736-2994

Abstract

Abstract: The paper is devoted to some selection theorems for set-valued stochastic integrals considered in papers by Kisielewicz et al. In particular, the Itô set-valued stochastic integrals are considered for absolutely summable countable subsets of the spaceL 2 ( [ 0, T ] × Ω, Σ F, R d × m ) of all square integrableF -nonanticipative matrix-valued stochastic processes. Such integrals are integrably bounded. Selection theorems, presented in the paper, cannot be considered for integrals defined by Jung and Kim in their paper forF -nonanticipative integrably bounded set-valued mappingsG : [ 0, T ] × Ω → R d × m, because such integrals are not in the general case integrably bounded.