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Malliavin calculus for Lie group-valued Wiener functions

Tai Melcher
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Abstract

Let G be a Lie group equipped with a set of left invariant vector fields. These vector fields generate a function ξon 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(ξ) is Malliavin differentiable to all orders and these derivatives belong to L^p(μ) for all p>1, where μis Wiener measure.

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Tai Melcher. 2009-02-05. Malliavin calculus for Lie group-valued Wiener functions. https://arxiv.org/abs/math/0508419

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