Markovian connection, curvature and Weitzenböck formula on Riemannian path spaces

DOI10.1006/jfan.2000.3719zbMath0980.58024OpenAlexW2031701707MaRDI QIDQ5933458

Shizan Fang

Publication date: 27 February 2002

Published in: Journal of Functional Analysis (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1006/jfan.2000.3719

zbMATH Keywords

stochastic differential equationspath spaceBochner-Weitzenböck formulainfinite-dimensional geometryRiemannian Brownian motion

Mathematics Subject Classification ID

Riemannian, Finsler and other geometric structures on infinite-dimensional manifolds (58B20) Diffusion processes and stochastic analysis on manifolds (58J65) Stochastic calculus of variations and the Malliavin calculus (60H07)

Related Items (1)

Stochastic calculus of variations and Harnack inequality on Riemannian path spaces

Cites Work

• The Ornstein-Uhlenbeck process over the space of Riemannian paths and the martingale problem
• The geometry of loop groups
• A Cameron-Martin type quasi-invariance theorem for Brownian motion on a compact Riemannian manifold
• The Lie bracket of adapted vector fields on Wiener spaces
• Stochastic analysis on the path space of a Riemannian manifold. I: Markovian stochastic calculus
• A probabilistic Weitzenböck formula on Riemannian path space
• Frame bundle of Riemannian path space and Ricci tensor in adapted differential geometry
• Renormalized differential geometry on path space: Structural equation, curvature
• Logarithmic Sobolev inequalities for pinned loop groups
• On the geometry of diffusion operators and stochastic flows
• Integration by parts formulas and dilatation vector fields on elliptic probability spaces

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