Space-time Wasserstein controls and Bakry-Ledoux type gradient estimates
Probability
2014-07-25 v2 Analysis of PDEs
Abstract
The duality in Bakry-\'Emery's gradient estimates and Wasserstein controls for heat distributions is extended to that in refined estimates in a high generality. As a result, we find an equivalent condition to Bakry-Ledoux's refined gradient estimate involving an upper dimension bound. This new condition is described as a -Wasserstein control for heat distributions at different times. The -version of those estimates are studied on Riemannian manifolds via coupling method.
Cite
@article{arxiv.1308.5471,
title = {Space-time Wasserstein controls and Bakry-Ledoux type gradient estimates},
author = {Kazumasa Kuwada},
journal= {arXiv preprint arXiv:1308.5471},
year = {2014}
}
Comments
35 pages(v1). 39 pages. The presentation of the proof of Proposition 3.6 is improved. The proof of Lemma 4.5 is corrected (Proposition 4.4 is added for this). The proof of Lemma 4.8 is modified (v2)