2. This question is on solving stochastic differential equations. The state variable Xt satisfies the stochastic differential equation dXt = -Y (log (Xt) - 0) Xtdt + oXtdWt, where the constants 0, o, y > 0. Consider a time T > t. Show that log XT = e Y(T-t) log X+ + ( 0 - 27 02 ) ( 1 - e 7 ( T -t ) ) to / e- 7( T - 3 ) dWs. [35 Marks] Using the results = E YSE [dW s] E (J. xaw.) " E calculate the mean and variance of log Xr when t - co. You should present full working at obtaining the mean and variance first. [25 Marks]