Let X be a Brownian motion directed by η, where the paths of η are strictly increasing a.s. Show that X(t) = B(η(t)), t ∈ R+, where B is a Brownian motion (on the same probability space as X and η)...

Let X be a Brownian motion directed by η, where the paths of η are strictly increasing a.s. Show that X(t) = B(η(t)), t ∈ R+, where B is a Brownian motion (on the same probability space as X and η) that is independent of η.