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.
Technical University, Institute of Mathematics, Podgórna 50, 65-246 Zielona Góra, Poland
Bibliografia
[1] J.P. Aubin, H. Frankowska, Set-Valued Analysis, Birkhauser, Boston 1990.
[2] G. Bocsan, On Wiener stochastic integral of a multifunction, Seminarul de Teoria Probabilitatilor si Applicatii, Univ. Timisoara 1987.
[3] H. Hess, On multivalued martingales whose values may be unbounded: martingale selectors and Mosco convergence, J. Multivar. Anal. 39 (1991), 175-201.
[4] F. Hiai, Multivalued stochastic integrals and stochastic differential inclusions, Division of Applied Mathematics, Research Institute of Applied Electricity, Sapporo 060, Japan, (preprint).
[5] F. Hiai, H. Umegaki, Integrals,conditional expectations,and martingales of multivalued functions, J. Multivar. Anal. 7 (1977), 149-182.
[6] M. Kisielewicz, Properties of solution set of stochastic inclusion, J. Appl. Math. Stoch. Anal. III, 6 (1993).
[7] M. Kisielewicz, Set-valued stochastic integrals and stochastic inclusions, Stoch. Anal. Appl. 16 (1) (1998) (in press).
[8] M. Kisielewicz, Differential Inclusions and Optimal Control, Kluwer-PWN 1991.
[9] M. Kisielewicz, W. Sosulski, Set-valued stochastic integrals over martingale measures and stochastic inclusions, Discuss. Math., 15 (2) (1995), 179-188.
[10] M. Michta, L. Rybiński, Selections of set-valued stochastic processes, J. Appl. Math. Stoch. Anal. (in press).
[11] J. Motyl, Note on strong solutions of a stochastic inclusion, J. Appl. Math. Stoch. Anal. III 8 (1995), 291-297.
[12] N.S. Papageorgiou, On the theory of Banach space valued multifunctions, 1 Integration and conditional expectation, J. Multivar. Anal. 17 (1985), 185-206.
[13] P. Protter, Stochastic Integration and Differential Equations, Springer-Verlag 1990.
[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.
[15] K. Przesławski, D. Yost, Lipschitz selections extentions and retractions, Quaderno 49 (1993), 1-18.
Typ dokumentu
Bibliografia
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