geometric Brownian motion.

geometric Brownian motion.
1. Letbe a geometric Brownian motion. Let p be a positive constant. Compute d ( SP ( t) ), the differential of S(t) raised to the power p.
2. (i) Compute dW4(t) and then write W4(T) as the sum of an ordinary (Lebesgue) integral with respect to time and an Ito integral.
(ii) Take expectations on both sides of the formula you obtained in (i), use the fact that 𝔼W2 (t) = t, and derive the formula 𝔼W4(T) = 3T2.
(iii) Use the method of (i) and (ii) to derive a formula for 𝔼W6(T)