Sequences of capacities, with connections to large-deviation theory

Journal of Theoretical Probability

Volumn 9, Issue 1, 1996, Pages 19-35

  O'Brien, George L ^a  

^a YORK UNIVERSITY   (Canada)

Author keywords

Capacities; Convergence of sequences; Large deviations; Narrow and vague topologies; Varadhan's integration theorem

Indexed keywords

EID: 21844498566     PISSN: 08949840     EISSN: None     Source Type: Journal    
DOI: 10.1007/BF02213733     Document Type: Article

References (25)

1. Berg, C., Christensen, J. P. R., and Ressel, P. (1984). Harmonic Analysis on Semigroups. Springer.
2. Billingsley, P. (1968). Convergence of Probability Measures. Wiley and Sons.
3. Bryc, W., and Dembo, A. (1993). Large deviations and strong mixing. Preprint.
4. Bucklew, J. A. (1990). Large Deviation Techniques in Decision, Simulation, and Estimation. Wiley and Sons.
5. Dellacherie, C., and Meyer, P.-A. (1978). Probabilities and Potential. Hermann and North Holland.
6. Dembo, A., and Zeitouni, O. (1993). Large Deviations Techniques and Applications. A. K. Peters, Wellesley, Massachusetts (Formerly published by Jones and Bartlett, Boston.)
7. Deuschel, J.-D., and Stroock, D. W. (1989). Large Deviations. Academic.
8. Dudley, R. M. (1966). Weak convergence of probabilities on nonseparable metric spaces and empirical measures on Euclidean spaces. Illinois J. Math. 10, 109-126.
9. Ellis, R. S. (1985). Entropy, Large Deviations and Statistical Mechanics. Springer-Verlag.
10. Gerritse, B. (1993). Varadhan's theorem for capacities. Report 9347, Department of Mathematics, Catholic University of Nijmegen.
11. Kallenberg, O. (1983). Random Measures. 2nd ed. Academic.
12. Lynch, J., and Sethuraman, J. (1987). Large deviations for processes with independent increments. Ann. Prob. 15, 610-627.
13. Norberg, T. (1986). Random capacities and their distributions. Prob. Th. Rel. Fields 73, 281-297.
14. (25)
15. O'Brien, G. L., and Vervaat, W. (1991). Capacities, large deviations and loglog laws. In Cambanis, S., Samorodnitsky, G., and Taqqu, M. (eds.), Stable Processes and Related Topics, Birkhauser, pp. 43-84.
16. O'Brien, G. L., and Vervaat, W. (1994). How subadditive are subadditive capacities? Commentationes Mathematicae Universitatis Carolinas 35, 311-324.
17. O'Brien, G. L., and Vervaat, W. (1995). Compactness in the theory of large deviations. Stochastic Processes and their Applications 57, 1-10.
18. O'Brien, G. L., and Watson, S. (1994). Narrow relative compactness of capacities. Preprint.
19. Parasarathy, K. R. (1967). Probability on Metric Spaces. Academic. New York.
20. Pukhalskii, A. A. (1991). On functional principle of large deviations. In New Trends in Probability and Statistics. Sazonov, V., and Shervashidze, T. (eds.), VPS/Mokslas, pp. 198-219.
21. Topsøe, F. (1970). Topology and Measure. Lecture Notes in Mathematics, Vol. 133. Springer-Verlag.
22. Varadhan, S. R. S. (1984). Large Deviations and Applications. SIAM.
23. Varadhan, S. R. S. (1966). Asymptotic properties and differential equations. Comm. Pure Appl. Math. 19, 261-286.
24. (25)].
25. Vervaat, W. (1995). Probability and Lattices, CWI Tract, Centrum voor Wiskunde en Informatika, Amsterdam (to appear).