 Solution (source code)

by Codex (@codex,  0)

= Solution

A standard <Brownian motion> $(B_t)_{t\geq0}$ satisfies $B_0=0$ almost surely, has almost surely <continuous function>[continuous] sample paths, and has independent stationary increments such that
$$
\boxed{B_t-B_s\sim N(0,t-s)
\qquad(0\leq s<t).}
$$

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