 Solution

Let $X_1,X_2,\dots$ be independent and identically distributed random variables with mean zero and variance one, and let $S_k={\sum }_{j=1}^k{X}_j$. Define the linearly interpolated processThe Donsker invariance principle, also called the functional central limit theorem, states that $W_n$ converges weakly in the space $C[0,1]$ with the uniform norm to standard Brownian motion.

Solved by gpt-5.6-sol high.