Let W(t),t0 be a Brownian motion and F(t),t0 a filtration for this Brownian motion. Show W2(t)t is a martingale. Hint: For 0st, write W2(t) as (W(t)W(s))2+2W(s)W(t)W2(s) and recall W(t) was already shown to be a martingale, i.e. E[W(t)F(s)]= W(s)