Integration by parts formulas and rotationally invariant Sobolev calculus on free loop spaces

DOI10.1016/0393-0440(93)90075-PzbMath0786.60074OpenAlexW2035217078MaRDI QIDQ687767

Rémi Léandre

Publication date: 6 December 1993

Published in: Journal of Geometry and Physics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/0393-0440(93)90075-p

zbMATH Keywords

Stratonovich stochastic differential equationfree loop spaceOrnstein- Uhlenbeck operator

Mathematics Subject Classification ID

Stochastic ordinary differential equations (aspects of stochastic analysis) (60H10)

Related Items (24)

COVER OF THE BROWNIAN BRIDGE AND STOCHASTIC SYMPLECTIC ACTION ⋮ A stochastic approach to the Euler-Poincaré number of the loop space of a developable orbifold ⋮ A class of vector fields on path spaces ⋮ STOCHASTIC PROCESSES ON CLASSIFYING SPACES AND STRING STRUCTURES ⋮ QUASI-REGULAR DIRICHLET FORMS ON FREE RIEMANNIAN PATH SPACES ⋮ Stochastic anticipative calculus on the path space over a compact Riemannian manifold ⋮ Integration by parts for heat kernel measures revisited ⋮ Asymptotics of spectral gaps on loop spaces over a class of Riemannian manifolds ⋮ Absence of spectral gaps on a class of loop spaces ⋮ Stochastic heat equations for infinite strings with values in a manifold ⋮ Stochastic Wess-Zumino-Witten model over a symplectic manifold ⋮ String structure over the Brownian bridge ⋮ THE STOCHASTIC LÉVY LAPLACIAN AND YANG–MILLS EQUATION ON MANIFOLDS ⋮ Differential calculus on path and loop spaces. II: Irreducibility of Dirichlet forms on loop spaces ⋮ Existence and uniqueness of geodesics on path spaces ⋮ Differentiable measures and the Malliavin calculus ⋮ Singular Integral Homology of the Stochastic Loop Space ⋮ Finite dimensional approximations to Wiener measure and path integral formulas on manifolds ⋮ Stochastic equivariant cohomologies and cyclic cohomology ⋮ Stochastic gauge transform of the string bundle ⋮ Representation of Green's function for the heat equation on a compact Lie group ⋮ Hilbert Space of Spinor Fields Over the Free Loop Space ⋮ Stochastic Cohomology of the Frame Bundle of the Loop Space ⋮ A unitary representation of the basical central extension of a loop group

Cites Work

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• Large deviations and the Malliavin calculus
• Differential forms on loop spaces and the cyclic bar complex
• Index theorem and equivariant cohomology on the loop space
• Stochastic calculus with anticipating integrands
• Sur le théorème d'Atiyah-Singer. (About the Atiyah-Singer theorem)
• Entire cyclic cohomology of Banach algebras and characters of \(\theta\)- summable Fredholm modules
• Integration on loop groups. II: Heat equation for the Wiener measure
• The odd Chern character in cyclic homology and spectral flow
• Invariant Sobolev calculus on the free loop space
• Iterated integrals of differential forms and loop space homology
• A Cameron-Martin Type Quasi-Invariance Theorem for Pinned Brownian Motion on a Compact Riemannian Manifold

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