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Probabilistic Potential Theory [PDF]

open access: yes, 2002
Consider a random subset K of ℝ d . A basic problem in probabilistic potential theory is the following: For what nonrandom sets E is ℙ(K ∩ E ≠ o) positive ? The archetypal example of such a set K is the range of a random field. Let X = (X t ; t ∈ ℝ + N ) denote an N-parameter stochastic process that takes its values in ℝ d and consider the random set K
Davar Khoshnevisan
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Probabilistic potential theory applied to electrical engineering problems

Proceedings of the IEEE, 1973
The mathematical equivalence between a potential satisfying a deterministic Laplace-type equation within a closed region and a certain probability associated with a particle exercising Brownian motion is described. Two methods are outlined for obtaining a potential by Brownian motion, the usual Monte Carlo method and a "number-diffusion" process.
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