## Tohoku Mathematical Journal

### Large deviations for random upper semicontinuous functions

#### Abstract

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

#### Article information

Source
Tohoku Math. J. (2), Volume 61, Number 2 (2009), 213-223.

Dates
First available in Project Euclid: 24 June 2009

https://projecteuclid.org/euclid.tmj/1245849444

Digital Object Identifier
doi:10.2748/tmj/1245849444

Mathematical Reviews number (MathSciNet)
MR2541406

Zentralblatt MATH identifier
1181.60039

#### Citation

Ogura, Yukio; Setokuchi, Takayoshi. Large deviations for random upper semicontinuous functions. Tohoku Math. J. (2) 61 (2009), no. 2, 213--223. doi:10.2748/tmj/1245849444. https://projecteuclid.org/euclid.tmj/1245849444

#### References

• J. W. S. Cassels, Measures of the non-convexity of sets and the Shapley-Folkman-Starr theorem, Math. Proc. Cambridge Philos. Soc. 78 (1975), 433--436.
• R. Cerf, Large deviations for sums of i.i.d. random compact sets, Proc. Amer. Math. Soc. 127 (1999), 2431--2436.
• A. Dembo and O. Zeitouni, Large deviations techniques and applications, Second Edition, Springer-Verlag, 1998.
• J. D. Deuschel and D. W. Stroock, Large deviations, Academic Press, 1989.
• M. D. Donsker and S. R. S. Varadhan, Asymptotic evaluation of certain Markov process expectations for large time III, Commun. Pure Appl. Math. 29 (1976), 389--461.
• M. Ledoux and M. Talagrand, Probability in Banach spaces, Springer-Verlag, 1991.
• S. Li, Y. Ogura and V. Kreinovich, Limit theorems and applications of set-valued and fuzzy set-valued random variables, Kluwer Academic Publishers, 2002.
• Y. Ogura, S. Li and X. Wang, Large and moderate deviations of random upper semicontinuous functions, to appear in Stoch. Anal. Appl.
• M. L. Puri and D. A. Ralescu, Limit theorems for random compact sets in Banach space, Math. Proc. Cambridge Philos. Soc. 97 (1985), 151--158.
• F. Treves, Topological vector spaces, Distributions and Kernels, Academic Press, New York, 1967.