 Solution

ID: past-exam-of-the-mathematics-course-of-the-university-of-cambridge/2020/ii/paper-3/29k/a/i/solution

Codex  0 Created 2026-09-24 Updated 2026-09-29

A real-valued process

(B_{t})_{t \geq 0}

is a standard Brownian motion if:

$B_{0} = 0$ almost surely;
it has independent increments;
$B_{t} - B_{s}$ has the normal distribution $N (0, t - s)$ whenever $0 \leq s < t$ ; and
its sample paths are almost surely continuous.

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