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?
Area enclosed by 2-dimensional random curve
10
$\begingroup$
stochastic-processes
brownian-motion
stochastic-integrals
stochastic-analysis
-
1Have you considered running a simulation of this to observe the empirical result? – 2012-12-15