9. Suppose that X(t) follows equation (9). Use Itos Lemma to verify that a solution to this...

9. Suppose that X(t) follows equation (9). Use Itˆo’s Lemma to verify that a solution to this differential equation is Xt

= X(0)e

−λt + α



1− e

−λt



+ σ

 t 0

eλ(s−t)dZs

(Hint: Note that when t increases by a small amount, the integral term changes by dZ(t).)