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

TL;DR

This paper establishes a necessary and sufficient condition for the strict convexity of the rate function of a random vector in , especially when the vector has a finite Laplace transform, and describes its effective domain under weaker conditions.

Contribution

It provides a complete characterization of when the rate function is strictly convex and describes its effective domain under less restrictive assumptions.

Findings

Strict convexity characterized by a necessary and sufficient condition.

Finite Laplace transform guarantees strict convexity.

Complete description of the effective domain under weaker conditions.

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.