Let \(W\) be a \(\mathbb{P}\)-Brownian motion, and \(B_{t}=W_{t}+u t\) be a \(\mathbb{Q}\)-Brownian motion, under a suitable change of probability. Check that, in the case \(u>0\), the process \(e^{W_{t}}\) tends towards 0 under \(\mathbb{Q}\) when \(t\) goes to infinity, whereas this is not the case under \(\mathbb{P}\).