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Hypoelliptic random heat kernels: A case study

Author: Richard B. Sowers
Journal: Proc. Amer. Math. Soc. 129 (2001), 2451-2460
MSC (1991): Primary 60H15
Published electronically: December 7, 2000
MathSciNet review: 1823931
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Abstract: We consider the fundamental solution of a simple hypoelliptic stochastic partial differential equation in which the first-order term is modulated by white noise. We derive some short-time asymptotic formulæ. We discover that the form of the dominant short-time asymptotics depends nontrivially upon the interplay between the geometry of the noisy first-order term and the geometry defined by the hypoelliptic operator.

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Additional Information

Richard B. Sowers
Affiliation: Department of Mathematics, University of Illinois, 1409 W. Green Street, Urbana, Illinois 60201

Keywords: Fundamental solution, hypoellipticity, stochastic PDE's
Received by editor(s): March 7, 1999
Received by editor(s) in revised form: December 6, 1999
Published electronically: December 7, 2000
Additional Notes: The author would like to thank the anonymous referee for a very careful reading of the manuscript. The author received support from NSF DMS-9726739 and NSF DMS-9615877 during the preparation of this work.
Communicated by: Claudia Neuhauser
Article copyright: © Copyright 2000 American Mathematical Society