## Show that a process is a Brownian motion

Question: Show that the process

$W(s) = \frac{\sqrt 2}{\pi} \sum^\infty_{j=1} \frac{sin[(j-\frac{1}{2})\pi s}{j- \frac{1}{2}} \zeta_j$

is a Brownian motion on [0,1].

No idea even where to start.