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arXiv · 2101.04246

Stochastic integrals and Brownian motion on abstract nilpotent Lie groups

Tai Melcher
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Abstract

We construct a class of iterated stochastic integrals with respect to Brownian motion on an abstract Wiener space which allows for the definition of Brownian motions on a general class of infinite-dimensional nilpotent Lie groups based on abstract Wiener spaces. We then prove that a Cameron--Martin type quasi-invariance result holds for the associated heat kernel measures in the non-degenerate case, and give estimates on the associated Radon--Nikodym derivative. We also prove that a log Sobolev estimate holds in this setting.

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Tai Melcher. 2021-01-12. Stochastic integrals and Brownian motion on abstract nilpotent Lie groups. https://doi.org/10.2969/jmsj%2F84678467

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