Let {B(t), t ≥ 0} be a standard Brownian motion, and define the process Y(t) = e−t B(e2t

), t ≥ 0; that is, {Y(t),t ≥ 0} is the Ornstein-Uhlenbeck process.

a. Show that Y(t) is a Gaussian process.

b. Find the covariance function of the process.