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Domain functionals and exit times for Brownian motion


Authors: Chaocheng Huang and David Miller
Journal: Proc. Amer. Math. Soc. 130 (2002), 825-831
MSC (1991): Primary 65J65; Secondary 58G32, 49K20
DOI: https://doi.org/10.1090/S0002-9939-01-06112-3
Published electronically: June 21, 2001
MathSciNet review: 1866038
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Abstract:

Two domain functionals describing the averaged expectation of exit times and averaged variance of exit times of Brownian motion from a domain, respectively, are studied. We establish the variational formulas for maximizing the functionals over $C^{k}$ domains with a volume constraint, and characterize the stationary points and maximizers.


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Additional Information

Chaocheng Huang
Affiliation: Department of Mathematics and Statistics, Wright State University, Dayton, Ohio 45435
Email: chuang@math.wright.edu

David Miller
Affiliation: Department of Mathematics and Statistics, Wright State University, Dayton, Ohio 45435
Email: dmiller@math.wright.edu

DOI: https://doi.org/10.1090/S0002-9939-01-06112-3
Keywords: Boundary value problems, Brownian motion, exit time, domain functionals, domain variations
Received by editor(s): May 24, 2000
Received by editor(s) in revised form: September 15, 2000
Published electronically: June 21, 2001
Communicated by: Claudia M. Neuhauser
Article copyright: © Copyright 2001 American Mathematical Society

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