Selection theorems for set-valued stochastic integrals
Michał Kisielewicz, Jerzy Motyl · Stochastic Analysis and Applications · 2019
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]×Ω→Rd×m, because such integrals are not in the general case integrably bounded.