Set-valued stationary processes

Journal of Multivariate Analysis

Volumn 63, Issue 1, 1997, Pages 180-198

  Wang, Rongming ^a   Wang, Zhenpeng ^a  

^a EAST CHINA NORMAL UNIVERSITY   (China)

Author keywords

Ergodicity; Law of large number; Set valued stationary processes; Stationary selection and representation

Indexed keywords

EID: 0031256594     PISSN: 0047259X     EISSN: None     Source Type: Journal    
DOI: 10.1006/jmva.1997.1702     Document Type: Article

References (22)

1. [1] Artstein, Z., and Vitale, R. A. (1975). A strong law of large numbers for random compact sets. Ann. Probab. 3 872-882.
2. [2] Artstein, Z. (1984). Limit Laws for Multifunctions Applied to an Optimization Problem, Springer-Verlag, Berlin/Heidelberg/New York/Tokyo. [Lecture Notes in Mathematics, Vol. 191]
3. [3] Aumann, R. J. (1965). Integrals of set-valued functions. J. Math. Anal. 12 1-12.
4. [4] Beck, A. (1963). On the strong law of large numbers. In Ergodic Theory (F. B. Wright, Ed.), pp. 21-53. Academic Press, New York.
5. [5] Castaing, C., and Valadier, M. (1977). Convex Analysis and Measurable Multifunctions, Springer-Verlag, Berlin/Heidelberg/New York. [Lecture Notes in Mathematics, Vol. 580]
6. [6] Cressie, N. (1978). A strong limit theorem for random sets. Suppl. Adv. Appl. Probab. 10 36-46.
7. [7] Cressie, N. (1979). Random set limit theorems. Adv. Appl. Probab. 11 281-282.
8. [8] Cressie, N. (1979). A central limit theorem for random sets. Z. Wahrsch. Verw. Geb. 49 37-47.
9. [9] Cressie, N., and Laslett, G. M. (1987). Random set theory and problems of modelling. SIAM Rev. 29 557-574.
10. [10] Guo, X. P., and Wang, R. M. (1996). Set-valued stationary processes with discrete parameter. J. East China Normal Univ. 2.
11. [11] Grenander, U. (1978). Pattern Analysis-Lectures in Pattern Theory I, Springer-Verlag, New York.
12. [12] Hiai, F. (1984). Strong laws of large numbers for multivalued random variables. In Lecture Notes in Mathematics, Vol. 1091, pp. 160-172. Springer-Verlag, Berlin/New York.
13. [13] Hiai, F. (1985). Convergence of conditional expectations and strong laws of large numbers for multivalued random variables. Trans. Amer. Math. Soc. 291 613-627.
14. [14] Hiai, F., and Umegaki, H. (1977). Integrals, conditional expectations and martingales of multivalued functions. J. Multivariate Anal. 7 149-182.
15. [15] Hindenbrand, W. (1974). Core and Equilibria of a Large Economy. Princeton Univ. Press, Princeton, NJ.
16. [16] Klein, E., and Thompson, A. (1984). Theory of Correspondences. Wiley, New York.
17. [17] Matheron, G. (1975). Random Sets and Integral Geometry. Wiley, London.
18. [18] Molchanov, I. S. (1991). Random sets: Survey on some results and applications. Ukrain. Math. J. 43 1477-1487.
19. [19] Papageorgiou, N. S. (1983). On the conditional expectation and convergence properties of random sets. Trans. Amer. Math. Soc. 347 2495-2512.
20. [20] Puri, M. L., and Ralescu, D. A. (1983). Strong law of large numbers for Banach space valued random. Ann. Probab. 11 222-224.
21. [21] Wang, R. M., and Wang, Z. P. (1996). Set-valued stationary processes with continuous parameters. (I). Correspondence relation. J. East China Normal Univ. 3.
22. [22] Wang, Z. P., and Xue, X. H. (1994). On convergence and closedness of multivalued martingales. Trans. Amer. Math. Soc. 341 807-827.