Discussiones Mathematicae Probability and Statistics 21(1) (2001) 63-75

SELECTION THEOREMS FOR STOCHASTIC SET-VALUED INTEGRALS

Michał Kisielewicz

Institute of Mathematics Technical University
Podgórna 50, 65-246 Zielona Góra, Poland

e-mail: m.kisielewicz@im.uz.zgora.pl

Abstract

Some special selections theorems for stochastic set-valued integrals with respect to the Lebesgue measure are given.

Keywords: stochastic set-valued integrals, nonanticipated stochastic processes, diagonal convexity, selections.

2000 Mathematics Subject Classiffication: 93E03, 93C30.

References

[1] M. Kisielewicz, Set-valued stochastic integrals and stochastic inclusions, Stoch. Anal. Appl. 15 (5) (1997), 783-800.
[2] M. Kisielewicz, Differential Inclusions and Optimal Control, Kluwer Acad. Publ., PWN, Dortrecht-Boston-London-Warszawa 1991.
[3] M. Kisielewicz, Weak compactness of solution set of stochastic differential inclusions, Topol. Meth. in Nonlin. Anal. (presented to print).
[4] L. Rybiński, On Carathéodory type selections, Fund. Math. 125 (1985), 187-193.

Received 3 February 2001