Probabilistic approach in potential theory to the equilibrium problem
Annales de l'Institut Fourier, Tome 23 (1973) no. 3, pp. 313-322.

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.

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.

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     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},
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Chung, Kai Lai. Probabilistic approach in potential theory to the equilibrium problem. Annales de l'Institut Fourier, Tome 23 (1973) no. 3, pp. 313-322. doi : 10.5802/aif.479. http://www.numdam.org/articles/10.5802/aif.479/

[1] M. Brelot, Les étapes et les aspects multiples de la théorie du potentiel, L'Enseignement mathématique, 58 (1972), 1-36. | MR | Zbl

[2] K. Ito and H.P. Mckean, Diffusion Processes and Their Sample Paths, Springer-Verlag, 1965. | MR | Zbl

[3] H.P. Mckean, A probabilistic interpretation of equilibrium charge distribution, J. Math. Kyoto Univ., 4 (1965), 617-623. | MR | Zbl

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