QUESTION 2 (23 marks) Suppose X, satisfies the Stochastic differential equation: dxt = (3 + 2t - 3 cos 3t) dt + XdWt. (a) Derive a stochastic differential equation for the process Y = 2te-3X Use appropriate substitutions, where necessary, to find the simpliest stochastic differential in terms of Y, only. (7 marks) (b) Derive a stochastic differential equation for the process Y = (X + 1) . Use appropriate substitutions, where necessary, to find the simpliest stochastic differential in terms of Y, only. (7 marks) (7 marks) (c) Find a solution for X, where X, is 2 at t = 0. (d) What is the solution for Y, for the stochastic differential equation derived in (b) where Yo = 81. (2 marks)