论文信息 - Large deviations for random upper semicontinuous functions

Large deviations for random upper semicontinuous functions

In this paper, we shall study large deviation principle for random upper semicontinuous functions, and obtain Cramer type theorems for those whose underlying space is a separable Banach space of type p.

Y. Ogura | T. Setokuchi

[1] F. Trèves. Topological vector spaces, distributions and kernels , 1967 .

[2] S. Varadhan,et al. Asymptotic evaluation of certain Markov process expectations for large time , 1975 .

[3] J. Cassels. Measures of the non-convexity of sets and the Shapley–Folkman–Starr theorem , 1975, Mathematical Proceedings of the Cambridge Philosophical Society.

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

[5] M. Talagrand,et al. Probability in Banach spaces , 1991 .

[6] Amir Dembo,et al. Large Deviations Techniques and Applications , 1998 .

[7] R. Cerf. Large deviations for sums of i.i.d. random compact sets , 1999 .

[8] V. Kreinovich,et al. Limit Theorems and Applications of Set-Valued and Fuzzy Set-Valued Random Variables , 2002 .

[9] Shoumei Li,et al. Large and Moderate Deviations of Random Upper Semicontinuous Functions , 2010 .

[10] S. Varadhan,et al. Large deviations , 2019, Graduate Studies in Mathematics.