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October, 2021 Stochastic integrals and Brownian motion on abstract nilpotent Lie groups
Tai MELCHER
Author Affiliations +
J. Math. Soc. Japan 73(4): 1159-1185 (October, 2021). DOI: 10.2969/jmsj/84678467

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.

Funding Statement

This research was supported in part by NSF Grants DMS-0907293 and DMS-1255574.

Citation

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Tai MELCHER. "Stochastic integrals and Brownian motion on abstract nilpotent Lie groups." J. Math. Soc. Japan 73 (4) 1159 - 1185, October, 2021. https://doi.org/10.2969/jmsj/84678467

Information

Received: 20 April 2020; Published: October, 2021
First available in Project Euclid: 22 June 2021

Digital Object Identifier: 10.2969/jmsj/84678467

Subjects:
Primary: 58J65
Secondary: 22E66 , 28D05 , 60H05 , 60J65

Keywords: heat kernel measure , infinite-dimensional Lie group , Logarithmic Sobolev inequality , Quasi-invariance

Rights: Copyright ©2021 Mathematical Society of Japan

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Vol.73 • No. 4 • October, 2021
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