Large and Moderate Deviations of Random Upper Semicontinuous Functions

Abstract

We firstly discuss the topological properties of the space of upper semicontinuous functions, and then we obtain large deviation principles for random upper semicontinuous functions under various topologies. Finally, we prove moderate deviation principles for random sets and random upper semicontinuous functions.

Keywords:

• Large deviations
• Moderate deviations
• Random sets
• Random upper semicontinuous functions

2000 Mathematics Subject Classification:

• 60F10
• 60F05

Y.O. was partially supported by Grant-in-Aid for Scientific Research 19540140. S.L. was partially supported by NSFC (No. 10771010), Research Fund of Beijing Educational Committee, and PHR (IHLB).

We thank the anonymous referees for their valuable comments. We are grateful to Professor David Elworthy for his numerous mathematical and linguistic corrections.