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.
"A scaling proof for Walsh's Brownian motion extended arc-sine law.." Electron. Commun. Probab. 17 1 - 9, 2012. https://doi.org/10.1214/ECP.v17-2319