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Consider a 2-dimensional Wiener process $(W_t)_{t \in [0,1]}$. Color every area which is enclosed by the line parametrised by $W_t$ (this means that, when the Wiener process makes a loop and intersects itself you color the points of the plane inside the loop). What is the expectation value of the area colored in that way?

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    Have you considered running a simulation of this to observe the empirical result?2012-12-15

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