Abstract
In 1950, Dvoretzky, Erdös and Kakutani [2] showed that in ℝ3almost all paths of Brownian motionXhave double points, or self-intersections of order 2 (there are no triple points [4]); later the same authors proved that almost all sample paths of Brownian motion in the plane have points of arbitrarily high multiplicity (a pointxin ℝ2is ak-tuple point for the path ω, or a self-intersection of orderk, if there are timestl<t2< … <tksuch thatx=X(t1, ω) =X(t2, ω) = …X(tk, ω)).
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