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A scaling proof for Walsh’s Brownian motion extended arc-sine law. (English) Zbl 1323.60115

Summary: 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 [Bull. Am. Math. Soc. 75, 1035–1036 (1969; Zbl 0266.60060)], 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.

MSC:

60J65 Brownian motion
60J60 Diffusion processes
60G52 Stable stochastic processes
60J70 Applications of Brownian motions and diffusion theory (population genetics, absorption problems, etc.)

Citations:

Zbl 0266.60060
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