Past exam of the mathematics course of the University of Cambridge / 2023 / iii / Paper 356 / 1 / e / Solution

At the reflecting endpoint the two values coincide:Under the diffusion limit of the telegraph process $s,\lambda \to \infty$ with $s^2/(2\lambda )=D$,Rapid velocity reversals erase directional persistence. Their integrated velocity converges to Brownian motion with diffusivity $D$, so its first-passage statistic converges to the zero-drift result.