Stochastic calculus of variations and Harnack inequality on Riemannian path spaces

DOI10.1016/S1631-073X(02)02561-XzbMath1030.60041WikidataQ115337241 ScholiaQ115337241MaRDI QIDQ1851446

Paul Malliavin, Ana Bela Cruzeiro

Publication date: 16 June 2003

Published in: Comptes Rendus. Mathématique. Académie des Sciences, Paris (Search for Journal in Brave)

zbMATH Keywords

Harnack inequalityRiemannian manifoldspath spacestochastic calculus of variations

Mathematics Subject Classification ID

Diffusion processes and stochastic analysis on manifolds (58J65) Stochastic calculus of variations and the Malliavin calculus (60H07) Existence of optimal solutions to problems involving randomness (49J55)

Related Items (2)

Finite dimensional approximation of Riemannian path space geometry. ⋮ Horizontal lift of Ornstein-Uhlenbeck process over Riemannian path space

Cites Work

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• The Ornstein-Uhlenbeck process over the space of Riemannian paths and the martingale problem
• Stochastic analysis on the path space of a Riemannian manifold. I: Markovian stochastic calculus
• Finite dimensional approximation of Riemannian path space geometry.
• 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
• Twisted sheets
• A Weitzenböck formula for the damped Ornstein–Uhlenbeck operator in adapted differential geometry
• Markovian connection, curvature and Weitzenböck formula on Riemannian path spaces
• Heat equation derivative formulas for vector bundles

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