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

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

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

The arrows in the PDF give

C_{i} \to C_{i + 1}

at rate

λ

,

W_{i} \to W_{i - 1}

at rate

μ

for

i \geq 1

C_{i} \to W_{i}

and

W_{i} \to C_{i}

α

and

β

. All rates are positive. One can travel upwards in level in the

C

phase and downwards in the

W

phase, switching at either end. Hence any state reaches any other through a finite positive-rate path: the continuous-time Markov chain is irreducible. Its total jump rates are uniformly bounded, so it is also nonexplosive.

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