Show that for any constant α where X(t) is defined as in exercise 7.19. Hint Make use of the moment generating function of the normal distribution. exercise 7.19 Let {S(t), t ≥ 0} be the standard...

Show that for any constant α

where X(t) is defined as in exercise 7.19.

Hint Make use of the moment generating function of the normal distribution.

exercise 7.19

Let {S(t), t ≥ 0} be the standard Brownian motion and

(1) Determine the covariance between S(t) and X(t).

(2) Verify that

Hint Make use of the fact that the random vector (S(t), X(t)) has a two-dimensional normal distribution.