Solution
= Solution
The <strong law for Brownian motion> gives $B_t/t\to0$ almost surely. Therefore
$$
\frac{\widetilde B_t}{t}=\frac{B_t}{t}-\mu\longrightarrow-\mu<0
$$
almost surely, and hence $\widetilde B_t\to-\infty$ almost surely.
= Solution
The <strong law for Brownian motion> gives $B_t/t\to0$ almost surely. Therefore
$$
\frac{\widetilde B_t}{t}=\frac{B_t}{t}-\mu\longrightarrow-\mu<0
$$
almost surely, and hence $\widetilde B_t\to-\infty$ almost surely.