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An Elementary Probabilistic Computation of the Poisson Kernel for the n = 2 and 3 Euclidean Ball

Published online by Cambridge University Press:  20 November 2018

Jacques Vauthier
Jacques Vauthier*
Affiliation:
Department of Mathematics, University of Toronto, Toronto, Canada, M5S1A1
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Abstract

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Direct and elementary derivation of the classical Poisson kernel for the ball in n = 2 or n = 3 dimensions starting with the usual expression involving the brownian motion bω, the stopping time T on the boundary, and Ex the conditional expectation on paths starting at x.

Keywords

kw60J4560J65Poisson kernelsBrownian motionMartingale
Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 27 , Issue 2 , 01 June 1984 , pp. 241 - 246
Copyright
Copyright © Canadian Mathematical Society 1984

References

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3. MacKean, H. P., Stochastic integrals, Academic Press (1969).Google Scholar
4. Greiner, P., Special harmonies on the Heisenberg group, Canadian Mathematical Bulletin Vol. 23 (1980), pp. 383–393.Google Scholar