Problem 4. Solving SDEs : Ornstein-Uhlenbeck process The purpose of this problem is to use Ito lemma to solve the Stochastic Differential Equation dXt = (a - X ) dt to dWt, with Xo = Co. The solution is known as an Ornstein-Uhlenbeck process. (a) Find an explicit expression for Xt. Hint: use the function f(t, x) = ex in Ito Formula. (b) Determine E[X ] and Var(X,). (c) Determine lim E[X ] and lim Var(Xt). 1-+00 1-+00 (d) Is X, normally distributed