A complete form of the classical theorem by Gauss-M. Riesz-Frostman is given for a large of Markov processes without the usual hypothesis of duality. The idea leads to a probabilistic solution of Robin’s problem and it is based on the last exit time from a transient set.
On donne une forme complète du théorème classique de Gauss-M. Riesz-Frostman pour une classe étendue de processus de Markoff, sans les hypothèses habituelles de dualité. L’idée mène à une solution probabiliste du problème de Robin et elle est basée sur le temps de la dernière sortie d’un ensemble transient.
@article{AIF_1973__23_3_313_0, author = {Chung, Kai Lai}, title = {Probabilistic approach in potential theory to the equilibrium problem}, journal = {Annales de l'Institut Fourier}, pages = {313--322}, publisher = {Institut Fourier}, address = {Grenoble}, volume = {23}, number = {3}, year = {1973}, doi = {10.5802/aif.479}, mrnumber = {52 #12098}, zbl = {0258.31012}, language = {en}, url = {http://www.numdam.org/articles/10.5802/aif.479/} }
TY - JOUR AU - Chung, Kai Lai TI - Probabilistic approach in potential theory to the equilibrium problem JO - Annales de l'Institut Fourier PY - 1973 SP - 313 EP - 322 VL - 23 IS - 3 PB - Institut Fourier PP - Grenoble UR - http://www.numdam.org/articles/10.5802/aif.479/ DO - 10.5802/aif.479 LA - en ID - AIF_1973__23_3_313_0 ER -
%0 Journal Article %A Chung, Kai Lai %T Probabilistic approach in potential theory to the equilibrium problem %J Annales de l'Institut Fourier %D 1973 %P 313-322 %V 23 %N 3 %I Institut Fourier %C Grenoble %U http://www.numdam.org/articles/10.5802/aif.479/ %R 10.5802/aif.479 %G en %F AIF_1973__23_3_313_0
Chung, Kai Lai. Probabilistic approach in potential theory to the equilibrium problem. Annales de l'Institut Fourier, Volume 23 (1973) no. 3, pp. 313-322. doi : 10.5802/aif.479. http://www.numdam.org/articles/10.5802/aif.479/
[1] Les étapes et les aspects multiples de la théorie du potentiel, L'Enseignement mathématique, 58 (1972), 1-36. | MR | Zbl
,[2] Diffusion Processes and Their Sample Paths, Springer-Verlag, 1965. | MR | Zbl
and ,[3] A probabilistic interpretation of equilibrium charge distribution, J. Math. Kyoto Univ., 4 (1965), 617-623. | MR | Zbl
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