Let X be a process with E(Xt) = 0 for all t ≥ 0 and independent increments (that is, Xt - Xs is independent from Is for any s, t, with 0 ≤ s < t < ∞).
(a) Show that X is a martingale.
(b) Suppose X has independent increments but that t → E(Xt) is not constant. Is X again a martingale? Justify your answer.