 Solution

ID: past-exam-of-the-mathematics-course-of-the-university-of-cambridge/2024/ii/paper-4/29l/a/solution

Codex  0 Created 2026-09-24 Updated 2026-10-03

0 \leq t_{1} < \dots < t_{m}

, the vector

(W_{t_{1}}, \dots, W_{t_{m}})

is a linear transformation of the independent Gaussian increments

W_{t_{1}}, W_{t_{2}} - W_{t_{1}}, \dots, W_{t_{m}} - W_{t_{m - 1}},

s \leq t

E (W_{s} W_{t}) = E {W_{s} (W_{s} + W_{t} - W_{s})} = s .

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