Regularity and stopping theorem for fuzzy martingales with continuous parameters

Information Sciences

Volumn 169, Issue 1-2, 2005, Pages 175-187

  Fei, Weiyin ^a  

^a ANHUI POLYTECHNIC UNIVERSITY   (China)

Author keywords

[No Author keywords available]

Indexed keywords

CONVERGENCE OF NUMERICAL METHODS; PARAMETER ESTIMATION; PROBABILITY; RANDOM PROCESSES; SET THEORY; STATISTICAL METHODS; THEOREM PROVING; TRAJECTORIES;

CONTINOUS PARAMETERS; DECOMPOSITION THEOREM; FUZZY MARTINGALES; RANDOM VARIABLES;

FUZZY CONTROL;

EID: 10844220554     PISSN: 00200255     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.ins.2004.02.011     Document Type: Article

References (20)

1. R. Alo, De.A. Korvin, C. Roberts, The optional sampling theorem for convex set-valued martingales, J. Reine Angew. Math. 310 (1979) 1-6.
2. S. Boswel, M. Talor, A central limits theorem for fuzzy random variables, Fuzzy Sets Syst. 24 (1987) 331-343.
3. W.Y. Fei, R.Q. Wu, Doob's stopping theorem for fuzzy (super, sub) martingales with discrete times, Fuzzy Sets Syst. 135 (2003) 377-390.
4. W.Y. Fei, R.Q. Wu, Doob's decomposition theorem for fuzzy (super) submartingales, Stoch. Anal. Appl. 22 (3) (2004) 627-645.
5. Y. Feng, Convergence theorems for fuzzy random variables and fuzzy martingales, Fuzzy Sets Syst. 102 (1999) 435-441.
6. S.W. He, J.G. Wang, J.A. Yan, Semimartingale Theory and Stochastic Calculus, Science Press-CRC Press Inc, Boca Raton, 1992.
7. C. Hess, On multivariate martingales whose values may be unbounded: martingale selectors and Mosoco convergence, J. Multiv. Anal. 39 (1991) 175-201.
8. F. Hiai, Convergence of conditional expectations and strong laws of large numbers for multivalued random variables, Trans. Am. Math. Soc. 291 (1985) 613-627.
9. F. Hiai, H. Umegaki, Integrals, conditional expectation and martingales of multivalued functions, J. Multiv. Anal. 7 (1977) 149-182.
10. E. Klement, M. Puri, D. Ralescu, Limit theorems for fuzzy random variables, Proc. R. Soc. Lond. A 407 (1986) 171-182.
11. V. Krätschmer, A unified approach to fuzzy random variables, Fuzzy Sets Syst. 123 (2001) 1-9.
12. R. Kruse, The strong law of large numbers for fuzzy random variables, Inform. Sci. 28 (1982) 233-241.
13. R. Kruse, K.D. Meyer, Statistics with Vague Data, Reidel, Dordrecht, 1987.
14. H. Kwakernaak, Fuzzy random variables I, Inform. Sci. 15 (1978) 1-29.
15. Y. Ogura, S. Li, Separability for graph convergence of sequences of fuzzy-valued random variables, Fuzzy Sets Syst. 123 (2001) 19-27.
16. N.S. Papageorgiou, On the theory of Banach space valued multifunctions.1. Integration and conditional expectation, 2. Set valued martingales and valued measures, J. Multiv. Anal. 17 (1985) 185-206, 207-227.
17. N.S. Papageorgiou, A convergence theorem for set valued supermartingales with values in a separable Banach space, Stoch. Anal. Appl. 5 (1987) 405-422.
18. M.L. Puri, D.A. Ralescu, Fuzzy random variables, J. Math. Anal. Appl. 114 (1986) 406-442.
19. M.L. Puri, D.A. Ralescu, Convergence theorem for fuzzy martingales, J. Math. Anal. Appl. 160 (1991) 107-122.
20. M. Stojaković, Fuzzy martingales - a simple form of fuzzy processes, Stoch. Anal. Appl. 14 (1996) 355-367.