Brownian beads

Abstract

We show that the past and future of half-plane Brownian motion at certain cutpoints are independent of each other after a conformal transformation. Like in Itô’s excursion theory, the pieces between cutpoints form a Poisson process with respect to a local time. The size of the path as a function of this local time is a stable subordinator whose index is given by the exponent of the probability that a stretch of the path has no cutpoint. The index is computed and equals 1/2.

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Cite this paper

@inproceedings{Virg2003BrownianB, title={Brownian beads}, author={B{\'a}lint Vir{\'a}g}, year={2003} }