@article{38f181047819450a9b1e315023e1d1a5,
title = "A simple proof of log-Sobolev inequalities on a path space with Gibbs measures",
abstract = "In this paper, we give a simple proof of log-Sobolev inequalities on an infinite volume path space C(ℝ, ℝd) with Gibbs measures. We introduce a parabolic stochastic partial differential equation which is reversible with respect to the Gibbs measures. In the proof, the gradient estimate for the diffusion semigroup which is derived from the stochastic flow plays a central role.",
keywords = "Gibbs measure, Gradient estimate, Log-Sobolev inequality, SPDE",
author = "Hiroshi Kawabi",
note = "Funding Information: I am grateful to Professor Tadahisa Funaki for sending me his manuscript Ref. 5 before publication. I also thank Professor Michael R{\"o}ckner for his interest and invitation to University of Bielefeld. The results of this paper were reported at Bielefeld and Bonn in Fall 2004. I was supported by Research Fellowships of the Japan Society for the Promotion of Science for Young Scientists and by Grant-in-Aid for Scientific research 15-3706, Japan Society for the Promotion of Science, Japan. Copyright: Copyright 2008 Elsevier B.V., All rights reserved.",
year = "2006",
month = jun,
doi = "10.1142/S021902570600238X",
language = "English",
volume = "9",
pages = "321--329",
journal = "Infinite Dimensional Analysis, Quantum Probability and Related Topics",
issn = "0219-0257",
publisher = "World Scientific Publishing Co. Pte Ltd",
number = "2",
}