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Stochastic integrals and Brownian motion on abstract nilpotent Lie groups

Tai Melcher

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.
Keywords: Brownian motion / nilpotent Lie / Stochastic integrals / Wiener space / Lie groups / abstract Wiener
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