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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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2. Levy, P., Le mouvement Brownien, Gauthier-Villars, Paris (1954).Google Scholar
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