This problem works out the missing steps in the proof of

Question

This problem works out the missing steps in the proof of Theorem 10.8. For W and X as defined in the proof of the theorem, show that W = AX. What is the matrix A? Use Theorem 5.16 to find f_W(w).

Theorem

For the Brownian motion process W(t), the joint PDF of W = [W(t₁), . . . , W(t_k)] is