An L2 theory for differential forms on path spaces I

Details An L2 theory for differential forms on path spaces I An L2 theory for differential forms on path spaces I

2006-12-14

arxiv.org/abs/math/0612416v1

Mathematics

Probability

Scientific paper

An L2 theory of differential forms is proposed for the Banach manifold of continuous paths on Riemannian manifolds M furnished with its Brownian motion measure. Differentiation must be restricted to certain Hilbert space directions, the H-tangent vectors. To obtain a closed exterior differential operator the relevant spaces of differential forms, the H-forms, are perturbed by the curvature of M. A Hodge decomposition is given for L2 H-one-forms, and the structure of H-two -forms is described. The dual operator d* is analysed in terms of a natural connection on the H-tangent spaces. Malliavin calculus is a basic tool.

Affiliated with

Also associated with

No associations

Rating

An L2 theory for differential forms on path spaces I does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with An L2 theory for differential forms on path spaces I, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and An L2 theory for differential forms on path spaces I will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-133178