Set-valued Stratonovich integral
Anna Góralczyk ; Jerzy Motyl
Discussiones Mathematicae Probability and Statistics, Tome 26 (2006), p. 63-81 / Harvested from The Polish Digital Mathematics Library

The purpose of the paper is to introduce a set-valued Stratonovich integral driven by a one-dimensional Brownian motion. We discuss the existence of this integral and investigate its properties.

Publié le : 2006-01-01
EUDML-ID : urn:eudml:doc:277051
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     title = {Set-valued Stratonovich integral},
     journal = {Discussiones Mathematicae Probability and Statistics},
     volume = {26},
     year = {2006},
     pages = {63-81},
     zbl = {1129.93045},
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Anna Góralczyk; Jerzy Motyl. Set-valued Stratonovich integral. Discussiones Mathematicae Probability and Statistics, Tome 26 (2006) pp. 63-81. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_7151_dmps_1075/

[000] [1] J.P. Aubin, Dynamic Economic Theory, A viability Approach, Springer, Verlag, Berlin 1997. | Zbl 0876.90032

[001] [2] J.P. Aubin and A. Cellina, Differential Inclusions, Noordhoff, Leyden 1984. | Zbl 0538.34007

[002] [3] J.P. Aubin and H. Frankowska, Set-valued analysis, Birkhäuser Boston-Basel-Berlin 1990. | Zbl 0713.49021

[003] [4] H.T. Banks and M.Q. Jacobs, A diffenertial calculus for set-valued function, J. Math. Anal. Appl. 29 (1970), 246-272. | Zbl 0191.43302

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

[005] [6] M. Hukuhara, Intégration des applications measurables dont a valeur est un compact convexe, Funkcialaj Ekvacioj 10 (1967), 205-223. | Zbl 0161.24701

[006] [7] M. Kisielewicz, Differential Inclusions and Optimal Control, Kluwer Acad. Publ.-PWN, Dordrecht-Boston-London Warszawa 1991. | Zbl 0731.49001

[007] [8] M. Kisielewicz, Set-valued stochastic integrals and stochastic inclusions, Stoch. Anal. Appl. 15 (5) (1997), 783-800. | Zbl 0891.93070

[008] [9] M. Kisielewicz, M. Michta and J. Motyl, Set-valued approach to stochastic control. Existence and regularity properties, Dynamic Syst. Appl. 12 (3-4) (2003), 405-432. | Zbl 1063.93047

[009] [10] M. Kisielewicz, M. Michta and J. Motyl, Set-valued approach to stochastic control. Viability and semimartingale issues, Dynamic Syst. Appl. 12 (3-4) (2003), 433-466. | Zbl 1064.93042

[010] [11] V. Lakshmikhantam, T. Gnana Bhaskar and D. Vasundhara, Theory of Set Differential Equations in Metric Space, (preprint) (2004).

[011] [12] P. Protter, Stochastic Integration and Differential Equations: A New Approach, Springer, New York 1990.

[012] [13] J. San Martin, One-dimensional Stratonovich differential equations, Ann. Probab. 21 (1) (1993), 509-553. | Zbl 0773.60049

[013] [14] E. Wong and M. Zakai, On the convergence of ordinary integrals to stochastic integrals, Ann. Math. Statist. 36 (1965), 1560-1564. | Zbl 0138.11201