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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 

 

Hypersurfaces in $\mathbb {R}^{d}$ and the variance
of exit times for Brownian motion


Authors: Kimberly K. J. Kinateder and Patrick McDonald
Journal: Proc. Amer. Math. Soc. 125 (1997), 2453-2462
MSC (1991): Primary 60J65, 58G32
MathSciNet review: 1401746
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Abstract: Using the first exit time for Brownian motion from a smoothly bounded domain in Euclidean space, we define two natural functionals on the space of embedded, compact, oriented, unparametrized hypersurfaces in Euclidean space. We develop explicit formulas for the first variation of each of the functionals and characterize the critical points.


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Additional Information

Kimberly K. J. Kinateder
Affiliation: Department of Mathematics and Statistics, Wright State University, Dayton, Ohio 45435-0001
Email: kjk@euler.wright.edu

Patrick McDonald
Affiliation: Department of Mathematics, University of South Florida, Sarasota, Florida

DOI: https://doi.org/10.1090/S0002-9939-97-03925-7
Keywords: Brownian motion, exit times, variance, variational calculus, free boundary problems
Received by editor(s): December 2, 1995
Received by editor(s) in revised form: March 5, 1996
Communicated by: Stanley Sawyer
Article copyright: © Copyright 1997 American Mathematical Society