Past exam of the mathematics course of the University of Cambridge / 2001 / iii / Paper 21 / 4 / d / Solution

False. The preceding interpolation argument proves that the event $\{B_t/t\to 0\}$ has probability one. Its complementary event, which is the nonconvergence assertion printed here, therefore has probability zero. The normalization by $t$ dominates both the integer-time increments and the fluctuations within each unit interval.