Hypoelliptic heat kernels on infinite-dimensional Heisenberg groups

Driver, Bruce; Eldredge, Nathaniel; Melcher, Tai

doi:10.1090/tran/6461

Hypoelliptic heat kernels on infinite-dimensional Heisenberg groups
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by Bruce K. Driver, Nathaniel Eldredge and Tai Melcher PDF

Trans. Amer. Math. Soc. 368 (2016), 989-1022 Request permission

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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