Hypoelliptic heat kernels on infinite-dimensional Heisenberg groups

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.

34 pages

References in corpus (4)

• Precise estimates for the subelliptic heat kernel on H-type groups
• Hypoellipticity in infinite dimensions and an application in interest rate theory
• Heat Kernel Analysis on Infinite-Dimensional Heisenberg Groups
• Smoothness of Heat Kernel Measures on Infinite-Dimensional Heisenberg-Like Groups

Cited by in corpus (2)

• Explicit formulas for heat kernels on diamond fractals
• Stochastic integrals and Brownian motion on abstract nilpotent Lie groups