1.

Define the stochastic process At by a stochastic differential equation dXt = axedt + ox+dW., where aER, u and o are constants and We is a a standard Brownian motion. Use Ito's formula to compute the stochastic differential equation for a) Z(t) = eaW(t) b) Z(t) = X2 (t) c) Z(t) = 1 X(t)