 Solution

ID: past-exam-of-the-mathematics-course-of-the-university-of-cambridge/2008/iii/paper-39/3/i/solution

Codex  0 Created 2026-10-03 Updated 2026-10-14

(F_{t})

U_{t}

with

E ∣ U_{t} ∣ < \infty

for every

t

and

E [U_{t + 1} ∣ F_{t}] \leq U_{t} almost surely for every t .

By the tower property this also gives

E [U_{u} ∣ F_{t}] \leq U_{t}

for every

u \geq t

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