Deviation inequalities and the law of iterated logarithm on the path space over a loop group

DOI10.1080/17442500500412399zbMath1086.60055OpenAlexW2055360854MaRDI QIDQ3368566

Xicheng Zhang, Nicolas Privault

Publication date: 31 January 2006

Published in: Stochastics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1080/17442500500412399

zbMATH Keywords

Brownian motionMalliavin calculusClark-Ocone formulaSample path properties

Mathematics Subject Classification ID

Brownian motion (60J65) Large deviations (60F10) Sample path properties (60G17) Loop groups and related constructions, group-theoretic treatment (22E67) Diffusion processes and stochastic analysis on manifolds (58J65) Stochastic integrals (60H05)

Cites Work

• Unnamed Item
• A uniform law of iterated logarithm for Brownian motion on compact Riemannian manifolds
• Range of fluctuation of Brownian motion on a complete Riemannian manifold
• Stochastic analysis on the path space of a Riemannian manifold. I: Markovian stochastic calculus
• Integration by parts and quasi-invariance for heat kernel measures on loop groups
• Integration by parts for heat measures over loop groups
• Integration by parts formula and logarithmic Sobolev inequality on the path space over loop groups
• Logarithmic Sobolev inequalities for pinned loop groups