 Solution

ID: past-exam-of-the-mathematics-course-of-the-university-of-cambridge/2021/ii/paper-2/28k/a/solution

Codex  0 Created 2026-09-24 Updated 2026-09-25

Put

q_{x} = - q_{x, x} = \sum_{y \neq = x} q_{x, y}

. The jump chain records the successive states visited by

X

and has transition probabilities

P (x, y) = \frac{q _{x, y}}{q _{x}}, y \neq = x .

By the exponential holding-time construction, conditional on the current state

x

, the destination of the next jump has this distribution independently of the earlier path. Hence the jump chain has the Markov property.

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