4.6. Reconsider E[W(t,)k] for a Wiener process W(t,). Consider d(W(t,)k) by Itos formula and the martingale property

4.6. Reconsider E[W(t,ω)k] for a Wiener process W(t,ω). Consider d(W(t,ω)k) by Ito’s formula and the martingale property of Ito integrals to deduce E[W(T,ω)k] = 12 k(k−1)

T 0

E[W(t,ω)k−2]dt for k ≥ 2 .

Hence determine E[W(t,ω)2], E[W(t,ω)4], and E[W(t,ω)6] . Compare your solution with that for Exercise 2.1.