Publications of the Research Institute for Mathematical Sciences

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Volume 23, Issue 2, 1987, pp. 251–264
DOI: 10.2977/prims/1195176539

Published online: 1987-04-30

On the Brownian Curve and its Circumscribing Sphere

Omer Adelman[1]

(1) Universite P. et M. Curie, Paris, France

The number of points the image of [0, t] under a planar Brownian motion has in common with its circumscribing circle does not have a zero-one law: it can be either two or three, both with a strictly positive probability. (This contradicts an assertion made by Paul Levy.)

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Adelman Omer: On the Brownian Curve and its Circumscribing Sphere. Publ. Res. Inst. Math. Sci. 23 (1987), 251-264. doi: 10.2977/prims/1195176539