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Selection theorems for set-valued stochastic integrals

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 of all square integrable -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 -nonanticipative integrably bounded set-valued mappings , because such integrals are not in the general case integrably bounded.