Representation theorems, set-valued and fuzzy set-valued Ito integral

Fuzzy Sets and Systems

Volumn 158, Issue 9, 2007, Pages 949-962

  Li, Shoumei ^a   Ren, Aihong ^a  

^a BEIJING UNIVERSITY OF TECHNOLOGY   (China)

Author keywords

Selection process; Set valued Ito integral; Set valued martingale; Set valued stochastic process

Indexed keywords

INTEGRAL EQUATIONS; NUMERICAL METHODS; RANDOM PROCESSES; THEOREM PROVING; VARIATIONAL TECHNIQUES;

SELECTION PROCESSS; SET VALUED ITO INTEGRALS; SET VALUED MARTINGALE; SET VALUED STOCHASTIC PROCESSES;

FUZZY SETS;

EID: 33947232258     PISSN: 01650114     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.fss.2006.12.004     Document Type: Article

References (29)

1. Ahmed N.U. Nonlinear stochastic differential inclusions on Banach space. Stochastic Anal. Appl. 12 (1994) 1-10
2. Aubin J.P., and Frankowska H. Set-Valued Analysis (1990), Birkhauser, Basel
3. Aubin J.P., and Prato G.D. The viability theorem for stochastic differential inclusions. Stochastic Anal. Appl. 16 (1998) 1-15
4. Aumann R. Integrals of set valued functions. J. Math. Anal. Appl. 12 (1965) 1-12
5. Beer G. Topologies on Closed and Closed Convex Sets (1993), Kluwer Academic Publishers, Dordrecht
6. Castaing C., and Valadier M. Convex analysis and measurable multifunctions, Lecture Notes in Mathematics vol. 580 (1977), Springer, Berlin, New York
7. Diamond P., and Kloeden P. Metric Spaces of Fuzzy Sets-Theory and Applications (1994), World Scientific, Singapore
8. Ikeda N., and Watanabe S. Stochastic Differential Equations and Diffusion Processes (1981), North-Holland, Kodansha, Tokyo
9. Jung E.J., and Kim J.H. On set-valued stochastic integrals. Stochastic. Anal. Appl. 21 2 (2003) 401-418
10. Hess C. On multivalued martingales whose values may be unbounded: martingale selectors and Mosco convergence. J. Multivariate Anal. 39 (1991) 175-201
11. Hiai F., and Umegaki H. Integrals, conditional expectations and martingales of multivalued functions. J. Multivariate Anal. 7 (1977) 149-182
12. Hu S., and Papageorgiou N.S. Handbook of Multivalued Analysis (1997), Kluwer Academic Publishers, Dordrecht
13. Karatzas I. Lectures on the Mathematics of Finance (1997), American Mathematical Society, Providence, RI, USA
14. Kim B.K., and Kim J.H. Stochastic integrals of set-valued processes and fuzzy processes. J. Math. Anal. Appl. 236 (1999) 480-502
15. Kisielewicz M. Existence theorem for nonconvex stochastic inclusions. J. Appl. Math. Stochastic Anal. 7 (1994) 151-159
16. Kisielewicz M. Viability theorems for stochastic inclusions. Discuss. Math. 15 (1995) 61-74
17. Kisielewicz M. Set-valued stochastic integrals and stochastic inclusions. Stochastic Anal. Appl. 15 (1997) 780-800
18. Kisielewicz M., Michta M., and Motyl J. Set valued approach to stochastic control part I (existence and regularity properties). Dynamic Systems Appl. 12 (2003) 405-432
19. Kisielewicz M., Michta M., and Motyl J. Set valued approach to stochastic control part II (viability and semimartingale issues). Dynamic Systems Appl. 12 (2003) 433-466
20. Klein E., and Thompson A.C. Theory of Correspondences Including Applications to Mathematical Economics (1984), Wiley, New York
21. S. Li, Martingale property of set-valued Ito integral, preprint, 2006.
22. S. Li, L. Guan, Decomposition and representation theorem of set-valued amarts, Internat. J. Approx. Reason., 2006, to appear.
23. Li S., and Ogura Y. Convergence of set valued sub- and super-martingales in the Kuratowski-Mosco sense. Ann. Probab. 26 (1998) 1384-1402
24. Li S., Ogura Y., and Kreinovich V. Limit Theorems and Applications of Set-Valued and Fuzzy Sets-Valued Random Variables (2002), Kluwer Academic Publishers, Dordrecht
25. Luu D.Q. Representations and regularity of multivalued martingales. Acta Math. Vietnam 6 (1981) 29-40
26. Motyl J. Stability problem for stochastic inclusion. Stochastic Anal. Appl. 16 (1998) 933-944
27. Oksendal B. Stochastic Differential Equations (1995), Springer, Berlin
28. Puri M.L., and Ralescu D.A. Fuzzy random variables. J. Math. Anal. Appl. 114 (1986) 406-422
29. Rogers L.C.G., and Williams D. Diffusions Markov Processes and Martingales, vol. 2: Ito Calculus (2000), Cambridge University Press, Cambridge