3.1. Show that Var[X(t)]=X20 e(2+2)te2t for X(t)=X0exp[(12 2)t+W(t)] . Give an example showing that even when

3.1. Show that Var[X(t)]=X20



e(2α+β2)t−e2αt

for X(t)=X0exp[(α−12

β2)t+βW(t)] .

Give an example showing that even when the expectation decays to zero, the variance may nonetheless grow in time.