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.
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Received: 23 January 1997 / Revised version: 21 January 1998
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Kinateder, K., McDonald, P. & Miller, D. Exit time moments, boundary value problems, and the geometry of domains in Euclidean space. Probab Theory Relat Fields 111, 469–487 (1998). https://doi.org/10.1007/s004400050174
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DOI: https://doi.org/10.1007/s004400050174