Exit Time Moments, Boundary Value Problems, and the Geometry of Domains in Euclidean Space
Document Type
Article
Publication Date
8-1-1998
Identifier/URL
40927318 (Pure)
Abstract
Let X t be a diffusion in Euclidean space. We initiate a study of the geometry of smoothly bounded domains in Euclidean space using the moments of the exit time for particles driven by X t , as functionals on the space of smoothly bounded domains. We provide a characterization of critical points for each functional in terms of an overdetermined boundary value problem. For Brownian motion we prove that, for each functional, the boundary value problem which characterizes critical points admits solutions if and only if the critical point is a ball, and that all critical points are maxima.
Repository Citation
Kinateder, K.,
McDonald, P.,
& Miller, D.
(1998). Exit Time Moments, Boundary Value Problems, and the Geometry of Domains in Euclidean Space. Probability Theory and Related Fields, 111 (4), 469-487.
https://corescholar.libraries.wright.edu/math/509
DOI
10.1007/s004400050174
