Past exam of the mathematics course of the University of Cambridge / 2008 / ii / Paper 2 / 26I / g / Solution

Combining the eigenvalue cases givesThis agrees with the interior drift: the switching phase spends proportions $\beta /(\alpha +\beta )$ and $\alpha /(\alpha +\beta )$ in $C$ and $W$, giving level drift $(\lambda \beta -\mu \alpha )/(\alpha +\beta )$. The harmonic calculation establishes recurrence even at the zero-drift boundary, rather than inferring it from drift alone.