When is the rate function of a random vector strictly convex?

Abstract

We give a necessary and sufficient condition for strict convexity of the rate function of a random vector in $R^d$. This condition is always satisfied when the random vector has finite Laplace transform. We also completely describe the effective domain of the rate function under a weaker condition.

This is version to be published. Some minor changes were made and a few references were added. The main result from the previous version was split into two parts, Theorems 1 and 2 in this version