Doob's stopping theorem for fuzzy (super, sub) martingales with discrete time

Fuzzy Sets and Systems

Volumn 135, Issue 3, 2003, Pages 377-390

  Fei, Weiyin ^a,b   Wu, Rangquan ^a   Shao, Shihuang ^a  

^a DONGHUA UNIVERSITY   (China)

^b ANHUI POLYTECHNIC UNIVERSITY   (China)

Author keywords

Doob's stopping theorem; Fuzzy (super sub) martingales; Fuzzy conditional expectation; Fuzzy random variable; Right closability

Indexed keywords

COMPUTER SIMULATION; DISCRETE TIME CONTROL SYSTEMS; FUZZY CONTROL; PROBABILISTIC LOGICS; PROBLEM SOLVING; SET THEORY; UNCERTAIN SYSTEMS;

FUZZY RANDOM VARIABLES;

FUZZY SETS;

EID: 0037401788     PISSN: 01650114     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0165-0114(02)00213-0     Document Type: Article

References (25)

1. Bán J. Radon-Nikodým theorem and conditional expectation of fuzzy-valued measures and variables. Fuzzy Sets and Systems. 34:1990;383-392.
2. Boswel S., Talor M. A central limits theorem for fuzzy random variables. Fuzzy Sets and Systems. 24:1987;331-343.
3. Diaz M.L., Gil M.A. Extension of Fubini's theorem for fuzzy random variables. Inform. Sci. 115:1999;29-41.
4. Feng Y. Mean-square integral and differential of fuzzy stochastic processes. Fuzzy Sets and Systems. 102:1999;271-280.
5. Feng Y. Convergence theorems for fuzzy random variables and fuzzy martingales. Fuzzy Sets and Systems. 103:1999;435-441.
6. He S.W., Wang J.G., Yan J.A. Semimartingale Theory and Stochastic Calculus. 1992;Science Press and CRC Press Inc. Boca Raton, Ann Arbor, London, Tokyo.
7. Hess C. On multivariate martingales whose values may be unbounded. martingale selectors and Mosoco convergence J. Multivariate Anal. 39:1991;175-201.
8. Hiai F. Convergence of conditional expectations and strong laws of large numbers for multivalued random variables. Trans. Amer. Math. Soc. 291:1985;613-627.
9. Hiai F., Umegaki H. Integrals, conditional expectation and martingales of multivalued functions. J. Multivariate Anal. 7:1977;149-182.
10. Klement E., Puri M., Ralescu D. Limit theorems for fuzzy random variables. Proc. Roy. Soc. London, A. 407:1986;171-182.
11. Kruse R. The strong law of large numbers for fuzzy random variables. Inform. Sci. 28:1982;233-241.
12. Kwakernaak H. Fuzzy random variables. Definition and theorems. Inform. Sci. 15:1978;1-29.
13. Li S., Ogura Y. Fuzzy random variables, conditional expectations and fuzzy valued martingales. J. Fuzzy Math. 4:1996;905-927.
14. S. Li, Y. Ogura, An optional sampling theorem for fuzzy valued martingales IFSA'97 Prague Proceedings, Vol. IV, 1997, pp. 9-14.
15. Papageorgiou N.S. A convergence theorem for set valued supermartingales with values in a separable Banach space. Stochastic Anal. Appl. 5(4):1987;405-422.
16. Papageorgiou N.S. Convergence and representation theorems for set-valued random processes. J. Math. Anal. Appl. 150:1990;129-145.
17. Papageorgiou N.S. On the conditional expectations and convergence properties of random sets. Trans. Amer. Math. Soc. 347:1995;2495-2515.
18. Puri M.L., Ralescu D.A. Fuzzy random variables. J. Math. Anal. Appl. 114:1986;406-422.
19. Puri M.L., Ralescu D.A. Convergence theorem for fuzzy martingales. J. Math. Anal. Appl. 160:1991;107-122.
20. Stojaković M. Fuzzy conditional expectation. Fuzzy Sets and Systems. 25(1):1992;53-61.
21. Stojaković M. Fuzzy martingales - a simple form of fuzzy processes. Stochastic Anal. Appl. 14(3):1996;355-367.
22. Wu H.C. Central limit theorems for fuzzy random variables. Inform. Sci. 15:1978;1-29.
23. Wu R.Q. Stochastic Differential Equations. 1985;Pitman, London.
24. Yoshida Y., Yasuda M., Nakagami J., Kurano M. Optimal stopping problems in a stochastic and fuzzy system. J. Math. Anal. Appl. 246:2000;135-149.
25. Zhang W.X., Wang Z.P., Gao Y. Set-valued Stochastic Processes. 1996;Science Press, Beijing. (in Chinese).