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Let $W$ be a Wiener process and $U_x$ is the amount of time spent below $x$ during time interval $(0,1)$. Hence $U_x=\int\limits_0^1I_{\{W(t). My question is: what is the probability density function of $U_x$? Thank you.

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    @ saz : my mistake, but I can't edit my comment. best regards.2012-12-13

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