Improvement of Wu's logarithmic Sobolev inequality via the Poisson-F\"ollmer process

TL;DR

This paper presents an alternative proof of Wu's logarithmic Sobolev inequality for the Poisson measure, utilizing a stochastic variational approach, which also allows for improvements under convexity assumptions.

Contribution

It introduces a new proof method for Wu's inequality and extends its applicability under convexity conditions.

Findings

Alternative proof of Wu's inequality using stochastic variational formula

Improved bounds under convexity assumptions

Enhanced understanding of entropy in Poisson measures

Abstract

We give an alternative proof to Wu's logarithmic Sobolev inequality for the Poisson measure on the nonnegative integers using a stochastic variational formula for entropy. We show that this approach leads to improvement of Wu's inequality under convexity assumptions.