 Solution

ID: past-exam-of-the-mathematics-course-of-the-university-of-cambridge/2024/ii/paper-2/30l/b/solution

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

The martingale property gives

E M_{n \land T} = E M_{0} = M_{0}

because

F_{0}

is trivial. Since

T < \infty

M_{n \land T} \to M_{T}

almost surely. The assumed uniform bound permits bounded convergence, so

E M_{T} = M_{0} .

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