Demonstrate, for the OrnsteinUhlenbeck process in (4.12), whose initial value is zero, that t is given by: Use this result to show that the serial

Demonstrate, for the Ornstein–Uhlenbeck process in (4.12), whose initial value is zero, that αt is given by:

Use this result to show that the serial covariance between

and is given by:

with

a(t) (1-e-2Kt) + Sek(s-t)dWs 2K