Advanced Studies in Pure Mathematics

Stochastic flows and geometric analysis on path spaces

K. David Elworthy

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Abstract

Some aspects of geometric analysis on path spaces are reviewed. Special emphasis is given to the relevance of stochastic flows to this analysis, and to the role of Ricci and higher order Weitzenböck curvatures. Path spaces of diffeomorphism groups and of compact symmetric spaces are considered.

Article information

Source
Probabilistic Approach to Geometry, M. Kotani, M. Hino and T. Kumagai, eds. (Tokyo: Mathematical Society of Japan, 2010), 61-78

Dates
Received: 16 February 2009
Revised: 24 March 2009
First available in Project Euclid: 24 November 2018

Permanent link to this document
https://projecteuclid.org/ euclid.aspm/1543086312

Digital Object Identifier
doi:10.2969/aspm/05710061

Mathematical Reviews number (MathSciNet)
MR2605411

Zentralblatt MATH identifier
1210.58029

Subjects
Primary: 58B10: Differentiability questions 58J65: Diffusion processes and stochastic analysis on manifolds [See also 35R60, 60H10, 60J60] 58A14: Hodge theory [See also 14C30, 14Fxx, 32J25, 32S35] 60H07: Stochastic calculus of variations and the Malliavin calculus 60H10: Stochastic ordinary differential equations [See also 34F05] 53C17: Sub-Riemannian geometry 58D20: Measures (Gaussian, cylindrical, etc.) on manifolds of maps [See also 28Cxx, 46T12] 58B15: Fredholm structures [See also 47A53]

Keywords
Path space stochastic analysis diffeomorphism group $L^2$ Hodge Theory Malliavin calculus Banach manifold differential forms curvature Weitzenböck symmetric space Bismut formulae

Citation

Elworthy, K. David. Stochastic flows and geometric analysis on path spaces. Probabilistic Approach to Geometry, 61--78, Mathematical Society of Japan, Tokyo, Japan, 2010. doi:10.2969/aspm/05710061. https://projecteuclid.org/euclid.aspm/1543086312


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