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Density of paths of iterated Levy transforms of Brownian motion

Marc Malric
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Abstract

The Levy transform of a Brownian motion B is the Brownian motion B't, the integral over (O,t) of sign of Bs with respect to dBs. Call T the corresponding transformation on the Wiener space W. We establish that a.s. the orbit of w in W under T is dense in W for the compact uniform convergence topology.

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Marc Malric. 2009-06-24. Density of paths of iterated Levy transforms of Brownian motion. https://arxiv.org/abs/math/0511154

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