Integration by parts formula and logarithmic Sobolev inequality on the path space over loop groups

DOI10.1214/aop/1022677382zbMath0946.60053OpenAlexW2087814230MaRDI QIDQ1807218

Shizan Fang

Publication date: 9 November 1999

Published in: The Annals of Probability (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1214/aop/1022677382

zbMATH Keywords

stochastic parallel transportintegration by partsmartingale representationtangent processes

Mathematics Subject Classification ID

Applications of stochastic analysis (to PDEs, etc.) (60H30) Diffusion processes and stochastic analysis on manifolds (58J65) Stochastic calculus of variations and the Malliavin calculus (60H07)

Related Items (6)

Metrics \(\mathcal H_s\) and behaviours as \(s\downarrow \frac {1} {2}\) on loop groups ⋮ Transportation cost inequalities on path and loop groups ⋮ Poincaré inequality for weighted first order Sobolev spaces on loop spaces ⋮ Deviation inequalities and the law of iterated logarithm on the path space over a loop group ⋮ LOGARITHMIC SOBOLEV INEQUALITY FOR $H_0^s$-METRIC ON PINNED LOOP GROUPS ⋮ Convergence of finite dimensional distributions of heat kernel measures on loop groups

Cites Work

• Integration on loop groups. I: Quasi invariant measures
• Large deviations and the Malliavin calculus
• The geometry of loop groups
• Logarithmic Sobolev inequalities on loop groups
• Integration on loop groups. II: Heat equation for the Wiener measure
• Integration on loop groups. III: Asymptotic Peter-Weyl orthogonality
• A Cameron-Martin type quasi-invariance theorem for Brownian motion on a compact Riemannian manifold
• Gaussian measures in Banach spaces
• Stochastic analysis on the path space of a Riemannian manifold. I: Markovian stochastic calculus
• De Rham-Hodge-Kodaira operator on loop groups
• Integration by parts and quasi-invariance for heat kernel measures on loop groups
• Martingale representation and a simple proof of logarithmic Sobolev inequalities on path spaces
• Renormalized differential geometry on path space: Structural equation, curvature
• Towards a Riemannian geometry on the path space over a Riemannian manifold
• Quasi-invariance of the Wiener measure on the path space over a compact Riemannian manifold
• Logarithmic Sobolev inequalities for pinned loop groups
• Uniqueness of ground states for Schrödinger operators over loop groups
• A class of integration by parts formulae in stochastic analysis I
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