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Articles

Selection theorems for set-valued stochastic integrals

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Pages 243-270 | Received 21 Aug 2018, Accepted 17 Nov 2018, Published online: 16 Jan 2019
 

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 space L2([0,T]×Ω,ΣF,Rd×m) of all square integrable F-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 for F-nonanticipative integrably bounded set-valued mappings G:[0,T]×ΩRd×m, because such integrals are not in the general case integrably bounded.

2001 MATHEMATICS SUBJECT CLASSIFICATION:

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