10 Problem 3. Let (Bt)t0 denote the Brownian motion and consider the Ito process

dX_t = X_tdt + X_tdB_t X₀ = 1, where and are constants, and > 0. We define the stochastic process Y_t by setting Y_t = (X_t)² for t 0.

(i) Determine the differential form of Y_t and show that Y_t is a geometrical Brownian motion.

(ii) Determine the mean E[exp Y_t] for t 0.