Let B(t), t ≥ 0, be a standard Brownian motion. Show that each of the following is a standard Brownian motion:

(1) (Scaling relation) a

−1B(a2t), t ≥ 0, where a = 0 is fixed.

(2) (Time inversion) W(t) = 0, t = 0 and tB(1/t), t > 0.