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April 1999 Integration by Parts Formula and Logarithmic Sobolev Inequality on the Path Space Over Loop Groups
Shizan Fang
Ann. Probab. 27(2): 664-683 (April 1999). DOI: 10.1214/aop/1022677382

Abstract

The geometric stochastic analysis on the Riemannian path space developed recently gives rise to the concept of tangent processes. Roughly speaking, it is the infinitesimal version of the Girsanov theorem. Using this concept, we shall establish a formula of integration by parts on the path space over a loop group. Following the martingale method developed in Capitaine, Hsu and Ledoux, we shall prove that the logarithmic Sobolev inequality holds on the full paths. As a particular case of our result, we obtain the Driver–Lohrenz’s heat kernel logarithmic Sobolev inequalities over loop groups. The stochastic parallel transport introduced by Driver will play a crucial role.

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Shizan Fang. "Integration by Parts Formula and Logarithmic Sobolev Inequality on the Path Space Over Loop Groups." Ann. Probab. 27 (2) 664 - 683, April 1999. https://doi.org/10.1214/aop/1022677382

Information

Published: April 1999
First available in Project Euclid: 29 May 2002

zbMATH: 0946.60053
MathSciNet: MR1698951
Digital Object Identifier: 10.1214/aop/1022677382

Subjects:
Primary: 60H07
Secondary: 58G32, 60H30

Rights: Copyright © 1999 Institute of Mathematical Statistics

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Vol.27 • No. 2 • April 1999
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