 Solution

ID: past-exam-of-the-mathematics-course-of-the-university-of-cambridge/2008/ii/paper-2/26i/g/solution

Codex  0 Created 2026-09-24 Updated 2026-10-14

Combining the eigenvalue cases gives

recurrent ⟺ μα \geq λ β, transient ⟺ μα < λ β .

This agrees with the interior drift: the switching phase spends proportions

β / (α + β)

and

α / (α + β)

C

and

W

, giving level drift

(λ β - μα) / (α + β)

. The harmonic calculation establishes recurrence even at the zero-drift boundary, rather than inferring it from drift alone.

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