Exercise 2. Prove that A = B = 0 as follows. Given a number h E R, define yt = at - h and consider the stochastic process yt. Since x is a Brownian motion, so is y; in fact, they have the same law: dy = dx = udt + odw, where w is a Wiener process (i.e., dw ~ N(0, dt) ) and yo = X0 - h. (1) Show that f(xt) = eth f(yt). (2) Show that, therefore, F(x t h) = eth F(x). (3) Subtracting F(x) from both sides and dividing by h -> 0, show that F'(x) = XF(x). (4) Conclude that F(x) must take the form Ker for some constant K