Suppose that B and B˜ are independent Brownian motions. Find the moment generating function of B˜(τ a ) at the time when B hits a, which is τ a = inf{t : B(t) = a}. Show that {B˜(τ a ) : a ∈ R+}...

Suppose that B and B˜ are independent Brownian motions. Find the moment generating function of B˜(τ_a) at the time when B hits a, which is τ_a
= inf{t : B(t) = a}. Show that {B˜(τ_a) : a ∈ R+} considered as a stochastic process has stationary independent increments.