When is the rate function of a random vector strictly convex?
Probability
2021-06-17 v2 Classical Analysis and ODEs
Abstract
We give a necessary and sufficient condition for strict convexity of the rate function of a random vector in . 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.
Keywords
Cite
@article{arxiv.2009.06809,
title = {When is the rate function of a random vector strictly convex?},
author = {Vladislav Vysotsky},
journal= {arXiv preprint arXiv:2009.06809},
year = {2021}
}
Comments
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