This is a question from course cs 335

Could you please help me solve this problem?

3. (12 marks) (Ito's Calculus) Suppose dZ is an increment of a standard Brownian motion. An Ito's process satisfies the following stochastic differential equation dX = a ( X, t) dt + b (X, t) dz. Ito's integral f, b(Z (t) , t) dZ (t) is the mean square limit of the Ito's sum, i.e. N-1 lim N-++00 b(Z (tn) , tn) (Z (tin+1) - Z (tn)) n=0 where tn is defined in (1). (a) Write down the Ito's sum for f, Z?dZ (t) where Z? is the square of Z (t). (b) What is the expected value of this Ito's sum? (c) Let Y (t) = e* +3Z(t) show that dY (t) = 2t + OIN Y (t) dt + 3Y (t) dZ (t)