论文信息 - Ergodic theorems for random compact sets and fuzzy variables in Banach spaces

Ergodic theorems for random compact sets and fuzzy variables in Banach spaces

Abstract The individual ergodic theorem is proved in two cases; first for compact set-valued random variable in a Banach space H of type p , p > 1; second for a random variable having values in the family of all fuzzy subsets of H . The set representation of fuzzy subsets is used. Three types of convergence of fuzzy variables are considered.

J. Bán

[1] Charles L. Byrne,et al. Remarks on the set-valued integrals of Debreu and Aumann , 1978 .

[2] G. Debreu. Integration of correspondences , 1967 .

[3] M. Puri,et al. Fuzzy Random Variables , 1986 .

[4] H. Rådström. An embedding theorem for spaces of convex sets , 1952 .

[5] J. Schwartz,et al. A vector-valued random ergodic theorem , 1957 .

[6] M. Puri,et al. Differentials of fuzzy functions , 1983 .

[7] Masaaki Miyakoshi,et al. An individual ergodic theorem for fuzzy random variables , 1984 .

[8] M. Puri,et al. Limit theorems for random compact sets in Banach space , 1985, Mathematical Proceedings of the Cambridge Philosophical Society.

[9] F. Hiai,et al. Integrals, conditional expectations, and martingales of multivalued functions , 1977 .

[10] K. Arrow,et al. General Competitive Analysis , 1971 .

[11] J. Bán. Radon-Nikody´m theorem and conditional expectation of fuzzy-valued measures and variables , 1990 .

[12] Rudolf Kruse. The strong law of large numbers for fuzzy random variables , 1982, Inf. Sci..

[13] F. Hiai. Radon-Nikodym theorems for set-valued measures , 1978 .

[14] Dan A. Ralescu,et al. Strong Law of Large Numbers for Banach Space Valued Random Sets , 1983 .

[15] R. Aumann. INTEGRALS OF SET-VALUED FUNCTIONS , 1965 .

[16] Henry Hermes,et al. Calculus of Set Valued Functions and Control , 1968 .

[17] P. Billingsley,et al. Convergence of Probability Measures , 1969 .