A scaling proof for Walsh's Brownian motion extended arc-sine law.

Stavros Vakeroudis (Université Libre de Bruxelles (ULB))
Marc Yor (Université Pierre et Marie Curie (UPMC) - Paris VI and Institut Universitaire de France (IUF))

Abstract


We present a new proof of the extended arc-sine law related to Walsh's Brownian motion, known also as Brownian spider. The main argument mimics the scaling property used previously, in particular by D. Williams, in the 1- dimensional Brownian case, which can be generalized to the multivariate case. A discussion concerning the time spent positive by a skew Bessel process is also presented.

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Pages: 1-9

Publication Date: December 31, 2012

DOI: 10.1214/ECP.v17-2319

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