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.References
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Additional Information
- Bruce K. Driver
- Affiliation: Department of Mathematics, University of California, San Diego, La Jolla, California 92093
- Email: bdriver@math.ucsd.edu
- Nathaniel Eldredge
- Affiliation: Department of Mathematics, Cornell University, Ithaca, New York 14853 – and – School of Mathematical Sciences, University of Northern Colorado, Greeley, Colorado 80639
- Email: neldredge@unco.edu
- Tai Melcher
- Affiliation: Department of Mathematics, University of Virginia, Charlottesville, Virginia 22904
- Email: melcher@virginia.edu
- Received by editor(s): December 12, 2013
- Published electronically: June 11, 2015
- Additional Notes: The first author’s research was supported in part by NSF Grant DMS-1106270.
The second author’s research was supported in part by NSF Grant DMS-0739164.
The third author’s research was supported in part by NSF Grants DMS-0907293 and DMS-1255574. - © Copyright 2015 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 368 (2016), 989-1022
- MSC (2010): Primary 58J35; Secondary 58J65, 60B15
- DOI: https://doi.org/10.1090/tran/6461
- MathSciNet review: 3430356