Brownian motions & Ito's lemma

1 a) If W, and W, are two independent Brownian motions and p is a constant between -1 and 1, then the process X, = pW, + v1 -p2W, is continuous and has marginal distributions N(0, /). Is this X, a Brownian motion? Explain why. b) Consider the general stochastic differential equation dG = A(G, ()dX + B(G, D)dr. Use Ito's lemma to show that it is possible to find a function f(G) which itself follows a random walk but with zero drift