Path Spaces and Their Tangent Spaces

  • Paul Malliavin
Part of the Grundlehren der mathematischen Wissenschaften book series (GL, volume 313)


Stochastic calculus of variation on a Lie group: Reduced variation and adjoint representation — Path groups: left infinitesimal quasi-invariance of Wiener measure — Path group on a compact Lie group — Orthonormal frame bundles over a Riemannian manifold: Levi-Civita parallelism, structure equations — Lifting to the frame bundle of the Riemannian diffusion: the stochastic parallel displacement — The horizontal stochastic flow, determination of its Jacobian on a Riemannian diffusion — Invariance of Brownian motion by orthogonal transformations — Tangent processes — Stochastic analysis on the path space of a Riemannian manifold: Twisted differential, Clark-Bismut-Ocone representation — Harnack estimates via the reduced variation — Loop spaces.


Vector Field Riemannian Manifold Tangent Space Loop Space Horizontal Flow 
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© Springer-Verlag Berlin Heidelberg 1997

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  • Paul Malliavin

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