 Recurrence of one-dimensional Brownian motion

ID: recurrence-of-one-dimensional-brownian-motion

One-dimensional Brownian motion satisfies

lim sup_{t \to \infty} B_{t} = + \infty, lim inf_{t \to \infty} B_{t} = - \infty

almost surely. Its continuous path therefore visits every point, including zero, infinitely often.

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