A probabilistic Weitzenböck formula on Riemannian path space

DOI10.1007/BF02791534zbMath0972.58012OpenAlexW2074898137WikidataQ115391582 ScholiaQ115391582MaRDI QIDQ1580486

Shizan Fang, Paul Malliavin, Ana Bela Cruzeiro

Publication date: 18 November 2001

Published in: Journal d'Analyse Mathématique (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/bf02791534

zbMATH Keywords

elliptic operatorgradient operatorRiemannian path spaceDe Rham-Hodge-Kodaira generator

Mathematics Subject Classification ID

Relations of PDEs with special manifold structures (Riemannian, Finsler, etc.) (58J60)

Related Items (5)

Finite dimensional approximation of Riemannian path space geometry. ⋮ An \(L^{2}\) theory for differential forms on path spaces. I ⋮ Markovian connection, curvature and Weitzenböck formula on Riemannian path spaces ⋮ Weak Levi-Civita connection for the damped metric on the Riemannian path space and vanishing of Ricci tensor in adapted differential geometry ⋮ Stochastic calculus of variations and Harnack inequality on Riemannian path spaces

Cites Work

• De Rham-Hodge-Kodaira's decomposition on an abstract Wiener space
• Stochastic anticipative calculus on the path space over a compact Riemannian manifold
• Stochastic analysis on the path space of a Riemannian manifold. I: Markovian stochastic calculus
• Renormalized differential geometry on path space: Structural equation, curvature
• Towards a Riemannian geometry on the path space over a Riemannian manifold
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