The 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

Past exam of the mathematics course of the University of Cambridge / 2024 / iii / Paper 201 / 4 / b / i / Solution

 Solution

ID: past-exam-of-the-mathematics-course-of-the-university-of-cambridge/2024/iii/paper-201/4/b/i/solution