Task 1 [10]. For which value of A, M(I) = Z"(t) - Azn-2(u)du is a martingale? ( is a Brownian Motion). Task 2 [20] .Two diffusion processes X and Y satisfy dX = (2 + 5t + X) dt + 3d21 dY = 48 dt + BY DZ1 + 6d22 Where 24 and 2, are two Brownian motions with p(21,22) = 0.2. By using the Ito's lemma, find dynamics of Y sin(x), Y.X, e'x and sin(Y) THE Task 1 [10]. For which value of A, M(I) = Z"(t) - Azn-2(u)du is a martingale? ( is a Brownian Motion). Task 2 [20] .Two diffusion processes X and Y satisfy dX = (2 + 5t + X) dt + 3d21 dY = 48 dt + BY DZ1 + 6d22 Where 24 and 2, are two Brownian motions with p(21,22) = 0.2. By using the Ito's lemma, find dynamics of Y sin(x), Y.X, e'x and sin(Y) THE