This is a continuation of With and Vi as in that problem, let (1) Prove thatW is a jointly normal Gaussian process with mean zero and Cov (Ws,Wt) = s∧t. (2) Use (6.10) and the Borel–Cantelli...

This is a continuation of With

and V_i
as in that problem, let

(1) Prove thatW is a jointly normal Gaussian process with mean zero and Cov (W_s,W_t) = s∧t.

(2) Use (6.10) and the Borel–Cantelli lemma to show that

converges uniformly over [0, 1]. Conclude that W is a Brownian motion.

Chapter 7