marks Ito calculus 3 marks Let X t and Y t be two stochastic processes such that dX x X t t dt ox X t t dZx dY uy Y t t dt oy Y t t dZy Xi 1 Xi Yi 1 Yi with dZx t dzy t being the increments for two distinct Wiener processes Zx t and Zy t Let X t X and Y ti Y Show that Xi 1Yi 1 XiYi Xi Yi 1 Yi Yi Xi 1 Xi Then using the definition of the Ito integral which is the limit of a discrete sum show that X s dy s XY Y s dx s dx s dY s