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.
Information
Published: 1 January 2010
First available in Project Euclid: 24 November 2018
zbMATH: 1210.58029
MathSciNet: MR2605411
Digital Object Identifier: 10.2969/aspm/05710061
Subjects:
Primary:
53C17
,
58A14
,
58B10
,
58B15
,
58D20
,
58J65
,
60H07
,
60H10
Keywords:
$L^2$ Hodge Theory
,
Banach manifold
,
Bismut formulae
,
curvature
,
diffeomorphism group
,
differential forms
,
Malliavin calculus
,
path space
,
Stochastic analysis
,
Symmetric space
,
Weitzenböck
Rights: Copyright © 2010 Mathematical Society of Japan
