Let (B_{t})_{t≥0} be a one-dimensional Brownian motion. Denote by , a, b > 0, the first entry time into the interval (-a, b)^{c}. We know from Corollary 5.11 that

We will now study the problem which probability distributions can be obtained in this way. More precisely, let X be a random variable with probability distribution function . We want to know if there is a Brownian motion (B_{t})_{t≥0} and a stopping time τ such that ...

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