## Arcsine laws and interval partitions derived from a stable subordinator (1992)

Venue: | Proc. London Math. Soc |

Citations: | 44 - 25 self |

### BibTeX

@ARTICLE{Pitman92arcsinelaws,

author = {Jim Pitman and Marc Yor},

title = {Arcsine laws and interval partitions derived from a stable subordinator},

journal = {Proc. London Math. Soc},

year = {1992},

pages = {65--326}

}

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### OpenURL

### Abstract

Le"vy discovered that the fraction of time a standard one-dimensional Brownian motion B spends positive before time t has arcsine distribution, both for / a fixed time when B, #0 almost surely, and for / an inverse local time, when B, = 0 almost surely. This identity in distribution is extended from the fraction of time spent positive to a large collection of functionals derived from the lengths and signs of excursions of B away from 0. Similar identities in distribution are associated with any process whose zero set is the range of a stable subordinator, for instance a Bessel process of dimension d for 1.