 Solution

ID: past-exam-of-the-mathematics-course-of-the-university-of-cambridge/2021/ii/paper-4/29k/b/solution

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

The transformed process is centred Gaussian and

E [W_{s} W_{t}] = s t min (1/ s, 1/ t) = min (s, t) .

The Brownian strong law makes

t W_{1/ t} \to 0

t ↓ 0

, giving continuity at zero; elsewhere continuity is immediate. Part (a) now applies.

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