The joint distributions of first hitting and last exit for Brownian motion (Q1895520)

Let \(B\) be a compact set in \(\mathbb{R}^ d\), the author gives a potential theoretic formula for the joint distribution of the first hitting time and the last hitting time of \(B\), and the positions at these times, of a Brownian motion in \(\mathbb{R}^ d\), and gives several consequences of this formula. In the case where \(B\) is a sphere centered at zero and the starting point of Brownian motion is zero, the formula can be made explicit.