Plane brownian motion in a region with holes |
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Authors: | Ma. Emilia Caballero |
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Affiliation: | (1) Instituto de Matemáticas, U.N.A.M., Circuito Exterior, Ciudad Universitaria, 04510, D.F. México, Mexico |
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Abstract: | We consider a fixed family of balls with decreasing radii in the plane. We establish a relationship between a Dirichlet problem in a region without the balls and the solution of a Schroedinger equation in the complete region. Then we find upper bounds for the probability that a brownian motion exits the region without touching these balls. This is used to study harmonic measure and entire functions. |
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Keywords: | Primary 60J65, 60J45 secondary 30D15, 31A15 |
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