Ruiz, J. R. Calcul probabiliste du noyau de Poisson de la sphère. (Probabilistic calculus of the Poisson kernel of the sphere). (French) Zbl 0625.60084 Ann. Sci. Univ. Clermont-Ferrand II 88, Probab. Appl. 5, 19-24 (1986). The Poisson kernel of the unit-sphere in \(R^ d\) is well known. In this paper, using a skew product representation of the d-dimensional Brownian motion by radial and angular parts, and then by the method of eigenfunction expansion of the generator of angular motion, the author gives a method of calculation of the Poisson kernel. Reviewer: Y.Ōshima MSC: 60J45 Probabilistic potential theory Keywords:Poisson kernel; eigenfunction expansion × Cite Format Result Cite Review PDF Full Text: Numdam EuDML References: [1] J. Vauthier ” An elementary probabilistic Computation of the Poisson Kernel for the n=2 and n=3 Euclidean Ball ”. Canad. Math. Bull. Vol. 27 ( 2 ), 1984 , 241 - 246 . MR 740421 | Zbl 0539.60083 · Zbl 0539.60083 · doi:10.4153/CMB-1984-035-3 [2] R.T. Seeley ” Spherical Harmonics ” Am. Math. Monthly (Slaught memorial paper n^\circ 11 ) Vol. 73 , ( 1966 ) 115 - 121 . MR 201695 | Zbl 0142.03503 · Zbl 0142.03503 · doi:10.2307/2313760 [3] D. Williams ” Diffusions, Markov Processes and Martingales ”. Vol. 1 . Wiley ( 1979 ). MR 531031 | Zbl 0826.60002 · Zbl 0826.60002 [4] K. Itô and H.P. Mc Kean , Jr. ” Diffusion Processes and their Sample Paths ”. Springer Verlag ( 1965 ). Zbl 0127.09503 · Zbl 0127.09503 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.