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Some properties of set-valued stochastic integrals of multiprocesses with finite Castaing representations

Kisielewicz M.

Commentationes Mathematicae

2013

Vol. 53, No. 2

113--126

The paper contains new properties of set-valued stochastic integrals defined as multifunctions with subtrajectory integrals equal to closed decomposable hulls of functional set-valued integrals defined in the author paper [8]. In particular, it is proved that such defined integrals for set-valued predictable square integrably bounded processes having finite Castaing representations are square integrably bounded. Up to now this property has not been proved. Unfortunately, in the general case the above boundedness problem is still open.