Logarithmic Sobolev inequality on free path space over a compact Riemannian manifold

Ling Pei

Statistics & Probability Letters, 2015, vol. 98, issue C, 12-19

Abstract: In this paper we use Bismut’s method to verify the formula of integration by parts on the free path space. By the formula, we verify the martingale representation for reference measure Pμ, the law of the Brownian motion on the base manifold with initial distribution μ. Then by the martingale representation we get the logarithmic Sobolev inequality on compact free Riemannian path space.

Keywords: Logarithmic Sobolev inequality; Integration by parts; Free path space; Martingale representation (search for similar items in EconPapers)
Date: 2015
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DOI: 10.1016/j.spl.2014.12.004

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