Arcsine Laws and Interval Partitions Derived from a Stable Subordinator

@inproceedings{Pitman2006ArcsineLA,
  title={Arcsine Laws and Interval Partitions Derived from a Stable Subordinator},
  author={Jim Pitman and Marc Yor},
  year={2006}
}
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… CONTINUE READING

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