August 2014
Intermediate to advanced
424 pages
11h 25m
English
Content preview from Brownian Motion, 2nd Edition
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14 Skorokhod representation
Let (Bt)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
(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 
. We want to know if there is a Brownian motion (Bt)t≥0 and a stopping time τ such that ...
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