Some applications of occupation times of Brownian motion with drift in mathematical finance.

Pechtl, Andreas

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Minimal thinness for subordinate Brownian motion in half-space

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We study minimal thinness in the half-space $H : = {x = (\tilde{x}, x_{d}) : \tilde{x} \in ℝ^{d - 1}, x_{d} > 0}$ for a large class of subordinate Brownian motions. We show that the same test for the minimal thinness of a subset of $H$ below the graph of a nonnegative Lipschitz function is valid for all processes in the considered class. In the classical case of Brownian motion this test was proved by Burdzy.