Exercise 14.3.11 Show that the transition probability density function p of dX=

−(1/2) Xdt +dW satisfies the backward equation

∂p

∂s

=−1 2

∂2 p

∂x2

+ 1 2

x

∂p

∂x

.

(Hint: X(t) ∼ N(xe−(t−s)/2, 1−e−(t−s)) when X(s) = x.)