Malliavin calculus for Lie group-valued Wiener functions
Probability
2009-02-06 v3
Abstract
Let G be a Lie group equipped with a set of left invariant vector fields. These vector fields generate a function \xi on Wiener space into G via the stochastic version of Cartan's rolling map. It is shown here that, for any smooth function f with compact support, f(\xi) is Malliavin differentiable to all orders and these derivatives belong to L^p(\mu) for all p>1, where \mu is Wiener measure.
Keywords
Cite
@article{arxiv.math/0508419,
title = {Malliavin calculus for Lie group-valued Wiener functions},
author = {Tai Melcher},
journal= {arXiv preprint arXiv:math/0508419},
year = {2009}
}
Comments
22 pages, 0 figures; final version with addition of example and significant reorganization, to appear in Infinite Dimensional Analysis and Quantum Probability