Let Ï(t) be a deterministic function such that Consider the process Use Ito's rule to show that this process satisfies dZ = ÏZdW. Deduce that

Let σ(t) be a deterministic function such that

Consider the process

Use Ito's rule to show that this process satisfies
dZ = σZdW.
Deduce that this process is a martingale process. Use this fact to find the moment-generating
Function
f(y) = E[eyX]
of the random variable

Finally, argue that X is normally distributed, with mean zero and variance

"IT 2(u)du is finite. x-S, (u)dW(u). 10 2 (u)du.