Geometric stochastic analysis on path spaces

zbMath1100.58014arXiv1911.09764MaRDI QIDQ5491003

Xue-Mei Li, K. David Elworthy

Publication date: 26 September 2006

Full work available at URL: https://arxiv.org/abs/1911.09764

zbMATH Keywords

Sobolev spacesMalliavin calculusstochastic differential equationsdifferential formsde Rham cohomologypath spaceabstract Wiener spacesconnectioninfinite dimensionsHodge-Kodaira theory

Mathematics Subject Classification ID

Stochastic ordinary differential equations (aspects of stochastic analysis) (60H10) Fredholm structures on infinite-dimensional manifolds (58B15) Diffusion processes and stochastic analysis on manifolds (58J65) Stochastic calculus of variations and the Malliavin calculus (60H07) Hodge theory in global analysis (58A14) Differentiability questions for infinite-dimensional manifolds (58B10) Sub-Riemannian geometry (53C17) Measures (Gaussian, cylindrical, etc.) on manifolds of maps (58D20)

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Momentum maps and stochastic Clebsch action principles ⋮ The vanishing of \(L^2\) harmonic one-forms on based path spaces ⋮ An \(L^{2}\) theory for differential forms on path spaces. I

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