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Brownian Motion, 2nd Edition by Björn Böttcher, Lothar Partzsch, René L. Schilling

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14 Skorokhod representation

Let (Bt)t≥0 be a one-dimensional Brownian motion. Denote by e9783110307290_i3125.jpg, a, b > 0, the first entry time into the interval (-a, b)c. We know from Corollary 5.11 that

e9783110307290_i3126.jpg

(14.1)

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 e9783110307290_i3127.jpg. We want to know if there is a Brownian motion (Bt)t≥0 and a stopping time τ such that ...

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