A de Bruijn identity for symmetric stable laws
Information Theory
2013-10-09 v1 math.IT
Probability
Abstract
We show how some attractive information--theoretic properties of Gaussians pass over to more general families of stable densities. We define a new score function for symmetric stable laws, and use it to give a stable version of the heat equation. Using this, we derive a version of the de Bruijn identity, allowing us to write the derivative of relative entropy as an inner product of score functions. We discuss maximum entropy properties of symmetric stable densities.
Cite
@article{arxiv.1310.2045,
title = {A de Bruijn identity for symmetric stable laws},
author = {Oliver Johnson},
journal= {arXiv preprint arXiv:1310.2045},
year = {2013}
}