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

Question:

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 $\mathbb{P}$.

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