Past exam of the mathematics course of the University of Cambridge / 2011 / ii / Paper 1 / 27J / iii / Solution

Starting from $+1$, the level reaches $c$ at time $c$ if the first holding time exceeds $c$. This has probability $e^{-ac}$; surviving beyond $c$ also makes the level strictly greater than $c$, as required by the strict event. A switch to $-1$ at time $u<c$ has density $q{e}^{-au}du$, leaves level $u$, and requires a later rise of $c-u$. Absorption before reaching $c$ cannot succeed. ThereforeHolding times have continuous distributions, so the single endpoint $u=c$ has no effect on the formula.