Let (B) be a Brownian motion and [begin{aligned}T_{a}^{(u)} & =inf left{t: B_{t}+u t=a ight} G_{a}^{(u)} & =sup

Let \(B\) be a Brownian motion and

\[\begin{aligned}T_{a}^{(u)} & =\inf \left\{t: B_{t}+u t=a\right\} \\G_{a}^{(u)} & =\sup \left\{t: B_{t}+u t=a\right\}\end{aligned}\]

Prove that

\[\left(T_{a}^{(u)}, G_{a}^{(u)}\right) \stackrel{\text { law }}{=}\left(\frac{1}{G_{u}^{(a)}}, \frac{1}{T_{u}^{(a)}}\right)\]

Give the law of the pair \(\left(T_{a}^{(u)}, G_{a}^{(u)}\right)\).