15.4 [Ornstein–Uhlenbeck process] Consider the process Xt = e−t Be2t , where Bt is a standard Brownian motion and the time corresponding to t in Xt is e2t for the Brownian motion.

a) Calculate E[Xt] and V(Xt).

b) Show that Xt has a normal distribution.

c) Show that Xt and X−t have the same finite dimensional distribution.