Stochastic integrals and Brownian motion on abstract nilpotent Lie groups
Probability
2022-04-26 v1
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.
Cite
@article{arxiv.2101.04246,
title = {Stochastic integrals and Brownian motion on abstract nilpotent Lie groups},
author = {Tai Melcher},
journal= {arXiv preprint arXiv:2101.04246},
year = {2022}
}