Note on the selection properties of set-valued semimartingales
Mariusz Michta
Discussiones Mathematicae, Differential Inclusions, Control and Optimization, Tome 16 (1996), p. 161-169 / Harvested from The Polish Digital Mathematics Library

Set-valued semimartingales are introduced as an extension of the notion of single-valued semimartingales. For such multivalued processes their semimartingale selection properties are investigated.

Publié le : 1996-01-01
EUDML-ID : urn:eudml:doc:275908
@article{bwmeta1.element.bwnjournal-article-div16i2n5bwm,
     author = {Mariusz Michta},
     title = {Note on the selection properties of set-valued semimartingales},
     journal = {Discussiones Mathematicae, Differential Inclusions, Control and Optimization},
     volume = {16},
     year = {1996},
     pages = {161-169},
     zbl = {0907.60049},
     language = {en},
     url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-div16i2n5bwm}
}
Mariusz Michta. Note on the selection properties of set-valued semimartingales. Discussiones Mathematicae, Differential Inclusions, Control and Optimization, Tome 16 (1996) pp. 161-169. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-div16i2n5bwm/

[000] [1] J.P. Aubin, H. Frankowska, Set-Valued Analysis, Birkhauser, Boston 1990.

[001] [2] G. Bocsan, On Wiener stochastic integral of a multifunction, Seminarul de Teoria Probabilitatilor si Applicatii, Univ. Timisoara 1987.

[002] [3] H. Hess, On multivalued martingales whose values may be unbounded: martingale selectors and Mosco convergence, J. Multivar. Anal. 39 (1991), 175-201. | Zbl 0746.60051

[003] [4] F. Hiai, Multivalued stochastic integrals and stochastic differential inclusions, Division of Applied Mathematics, Research Institute of Applied Electricity, Sapporo 060, Japan, (preprint).

[004] [5] F. Hiai, H. Umegaki, Integrals,conditional expectations,and martingales of multivalued functions, J. Multivar. Anal. 7 (1977), 149-182. | Zbl 0368.60006

[005] [6] M. Kisielewicz, Properties of solution set of stochastic inclusion, J. Appl. Math. Stoch. Anal. III, 6 (1993).

[006] [7] M. Kisielewicz, Set-valued stochastic integrals and stochastic inclusions, Stoch. Anal. Appl. 16 (1) (1998) (in press).

[007] [8] M. Kisielewicz, Differential Inclusions and Optimal Control, Kluwer-PWN 1991. | Zbl 0731.49001

[008] [9] M. Kisielewicz, W. Sosulski, Set-valued stochastic integrals over martingale measures and stochastic inclusions, Discuss. Math., 15 (2) (1995), 179-188. | Zbl 0849.93058

[009] [10] M. Michta, L. Rybiński, Selections of set-valued stochastic processes, J. Appl. Math. Stoch. Anal. (in press). | Zbl 0910.60030

[010] [11] J. Motyl, Note on strong solutions of a stochastic inclusion, J. Appl. Math. Stoch. Anal. III 8 (1995), 291-297. | Zbl 0831.93061

[011] [12] N.S. Papageorgiou, On the theory of Banach space valued multifunctions, 1 Integration and conditional expectation, J. Multivar. Anal. 17 (1985), 185-206. | Zbl 0579.28009

[012] [13] P. Protter, Stochastic Integration and Differential Equations, Springer-Verlag 1990. | Zbl 0694.60047

[013] [14] K. Przesławski, Linear selectors and valuations for the family of compact and convex sets in Eucalideau vector space, Ph. D. Thesis, UAM, Poznań 1986.

[014] [15] K. Przesławski, D. Yost, Lipschitz selections extentions and retractions, Quaderno 49 (1993), 1-18.