Financial Engineering question:

Problem 3. ( 25 pts) Let u : (0,T] x R H R be a smooth solution to the heat equation 1 22u + at 2 a.x2 0. Show that ut, Bt) is a martingale where B is a Brownian motion. Problem 3. ( 25 pts) Let u : (0,T] x R H R be a smooth solution to the heat equation 1 22u + at 2 a.x2 0. Show that ut, Bt) is a martingale where B is a Brownian motion