Year: 2024
Type: article
Abstract: We formulate a new information-theoretic principle—the shifted composition rule—which bounds the divergence (e.g., Kullback-Leibler or Rényi) between the laws of two stochastic processes via the introduction of auxiliary shifts. In this paper, we apply this principle to prove reverse transport inequalities for diffusions which, by duality, imply F.-Y. Wang’s celebrated dimension-free Harnack inequalities. Our approach bridges continuous-time coupling methods from geometric analysis with the discrete-time shifted divergence technique from differential privacy and sampling. It also naturally gives rise to (1) an alternative continuous-time coupling method based on optimal transport, which bypasses Girsanov transformations, (2) functional inequalities for discrete-time processes, and (3) “reverse” Harnack inequalities.
Authors: Jason M. Altschuler, Sinho Chewi
Institutions: University of Pennsylvania, Yale University
Language: English
Subfield: Applied Mathematics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
Funder: Institute for Advanced Study
OpenAlex ID: W4403183092