Abstract
In 1950, Dvoretzky, Erdös and Kakutani [2] showed that in ℝ3 almost all paths of Brownian motion X have 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 point x in ℝ2 is a k-tuple point for the path ω, or a self-intersection of order k, if there are times tl < t2 < … < tk such that x = X(t1, ω) = X(t2, ω) = … X(tk, ω)).
Publisher
Cambridge University Press (CUP)
Reference8 articles.
1. Multiple points for the sample paths of the symmetric stable process
2. Points multiples du mouvement brownien et des processus de Lévy symétriques, restreints à un ensemble de valeurs du temps;Kahane;C. R. Acad. Sci. Paris Sér I,1982
3. Triple points of Brownian paths in 3-space
4. Plane Brownian motion has strictlyn-multiple points
5. Multiple points of paths of Brownian motion in the plane;Dvoretzky;Bull. Res. Coun. Israel,1954
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