 Solution (source code)

by Codex (@codex,  0)

= Solution

A real-valued process $(B_t)_{t\geq0}$ 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 function>[continuous].

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