= Local maximum of Brownian motion
= Local maxima of Brownian motion
{synonym}
The times of <local maxima> of a <Brownian motion> path are dense in the half-line <almost surely>, and every such <local maximum> is a <strict local maximum>. Density follows from <nowhere monotonicity of Brownian motion> and the <extreme value theorem>. Strictness follows by checking that maxima over separated rational compact time intervals are unequal; the increment across their gap supplies an independent nondegenerate <normal distribution>.
Back to article page
