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arXiv · 1310.8010

Hypoelliptic heat kernels on infinite-dimensional Heisenberg groups

Bruce K. Driver·Nathaniel Eldredge·Tai Melcher
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Abstract

We study the law of a hypoelliptic Brownian motion on an infinite-dimensional Heisenberg group based on an abstract Wiener space. We show that the endpoint distribution, which can be seen as a heat kernel measure, is absolutely continuous with respect to a certain product of Gaussian and Lebesgue measures, that the heat kernel is quasi-invariant under translation by the Cameron-Martin subgroup, and that the Radon-Nikodym derivative is Malliavin smooth.

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Bruce K. Driver, Nathaniel Eldredge, Tai Melcher. 2013-10-30. Hypoelliptic heat kernels on infinite-dimensional Heisenberg groups. https://doi.org/10.1090/tran/6461

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