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Please use this identifier to cite or link to this item: https://dspace.lboro.ac.uk/2134/2440

Title: Ito maps and analysis on path spaces
Authors: Elworthy, K.D.
Li, Xue-Mei
Issue Date: 2006
Abstract: We consider versions of Malliavin calculus on path spaces of compact manifolds with diffusion measures, defining Gross-Sobolev spaces of differentiable functions and proving their intertwining with solution maps, I, of certain stochastic differential equations. This is shown to shed light on fundamental uniqueness questions for this calculus including uniqueness of the closed derivative operator d and Markov uniqueness of the associated Dirichlet form. A continuity result for the divergence operator by Kree and Kree is extended to this situation. The regularity of conditional expectations of smooth functionals of classical Wiener space, given I, is considered and shown to have strong implications for these questions. A major role is played by the (possibly sub-Riemannian) connections induced by stochastic differential equations: Damped Markovian connections are used for the covariant derivatives.
Description: This is a pre-print.
URI: https://dspace.lboro.ac.uk/2134/2440
Appears in Collections:Pre-prints (Maths)

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