Solution
= Solution
The one-dimensional <Donsker invariance principle> says that if $X_1,X_2,\ldots$ are <IID random variables> with mean zero and variance one, then the linearly interpolated process
$$
W_n(t)=\frac1{\sqrt n}\left(S_{\lfloor nt\rfloor}+(nt-\lfloor nt\rfloor)X_{\lfloor nt\rfloor+1}\right),
\qquad0\leq t\leq1,
$$
converges weakly in $C([0,1])$ with the uniform norm to standard <Brownian motion>.