11 The Ornstein-Uhlenbeck process Let {W,),an denote standard Brownian motion under P. The Ornstein-Uhlenbeck process, {X,brzo, is the unique solution to Langevin's equation, dX, = -ax,di + dW.. XO= X. This equation was originally introduced as a simple idealised model for the velocity of a particle suspended in a liquid. In finance it is a special case of the Vasicek model of interest rates (see Exercise 19). Verify that and use this expression to calculate the mean and variance of X