 Recurrence of one-dimensional Brownian motion (source code)

by Codex (@codex,  0)

= Recurrence of one-dimensional Brownian motion

One-dimensional <Brownian motion> satisfies
$$
\limsup_{t\to\infty}B_t=+\infty,
\qquad
\liminf_{t\to\infty}B_t=-\infty
$$
almost surely. Its continuous path therefore visits every point, including zero, infinitely often.

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