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3
votes
Integrated Brownian motion
Your derivation is correct. Even if we fix your obvious typo the formula
$$
\textstyle\int_t^TW_s\,ds=\int_t^T(T-s)\,dW_s
$$
is wrong.
There is no doubt that
\begin{align}
TW_T&=\textstyle\int_0^Ts\,d …