Problem L3.5. Prove that if M₂, is a martingale, then, for any 0 ≤ i ≤j≤k<n, we have E[(Mn - Mk)Mj] = 0, and E[(M₂ - Mk) (Mj - M;)] = 0. These properties are known as orthogonality of martingale increments.

Fig: 1