Brownian excursions and minimal thinness, I. (English) Zbl 0656.60051

By means of a careful estimation of capacity, the author derives an integral-type criterion for thinness (regularity with respect to Brownian motion) for a class of sets arising naturally in Lipschitz domain problems. Minimal thinness (regularity with respect to \(h\)-conditioned Brownian motion) is then related to the behaviour of an excursion law for Brownian motion, and this is used to provide connections between minimal thinness and thinness, and an associated integral test.
Reviewer: W.S.Kendall


60G17 Sample path properties
60J65 Brownian motion
60J50 Boundary theory for Markov processes
31B25 Boundary behavior of harmonic functions in higher dimensions
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