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

• Autorzy: Kisielewicz M.

Identyfikatory

DOI

10.14708/cm.v53i2.787

• Języki publikacji: EN

Abstrakty

EN

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.

Słowa kluczowe

EN

set-valued mappings; set-valued integrals; set-valued stochastic processes

• Wydawca: Polskie Towarzystwo Matematyczne
• Czasopismo: Commentationes Mathematicae
• Rocznik: 2013
• Tom: Vol. 53, No. 2
• Strony: 113--126
• Opis fizyczny: Bibliogr. 10 poz.

Twórcy

autor

Kisielewicz M.

• University of Zielona Góra, Faculty of Mathematics Computer Science and Econometrics, Podgórna 50, 65–246 Zielona Góra, Poland

Bibliografia

• [1] G. Bocsan, On Wiener stochastic integrals of multifunctions, Univ. Tim. FSN, 87 (1987), 1-7.
• [2] F. Hiai, Multivalued stochastic integrals and stochastic inclusions, not publisched.
• [3] F. Hiai and H. Umegaki, Integrals, Conditional Expections, and Martingales of Multivalued Functions, J. Multivariate Analalysis 7 (1977), 149 - 182.
• [4] Sh. Hu and N.S. Papageourgiou, Handbook of Multivalued Analysis I, Kluwer Academic Publishers, 1997.
• [5] J. Jacod and A.N. Shiryaev, Limit Theorems for Stochastic Processes, Springer-Verlag, Berlin - Heidelberg, 1987.
• [6] E.J. Jung and J.H. Kim, On Set-Valued Stochastic Integrals, Stochastic Analysis and Appl. 21(2) (2003), 401 - 418 .
• [7] B. K. Kim and J. H. Kim, Stochastic Integrals of Set-Valued Prosesses and Fuzzy Processes, J. Math. Anal. Appl. 2336 (1999) 480 -502.
• [8] M. Kisielewicz, Set-valued stochastic integrals and stochastic inclusions, Discuss. Math. 15 (1995), 61 - 74.
• [9] M. Kisielewicz, Set-valued stochastic integrals and stochastic inclusions, Stoch. Anal. Appl. 15(5)(1997), 783 - 800.
• [10] M. Kisielewicz, Some properties of set – valued stochastic integrals, J. Math. Anal. Appl. 388 (2012), 984 – 995.