LARGE DEVIATIONS ON LINEAR SPACES
George L. O’Brien
Jiaming Sun
Abstract: We discuss a method, which we call the expansion method, for proving large
deviation principles and bounds. The method is applicable on general topological spaces but
our main application is to prove a large deviation result for a sequence of random vectors
taking values in a real locally convex linear space. As applications of this result, two general
Cramér-type theorems are given. One comes directly from the main result; the proof
of the other involves truncation and a continuity property of convex conjugation.
2000 AMS Mathematics Subject Classification: Primary: -; Secondary: -;
Key words and phrases: -