RANDOM DISCRETE DISTRIBUTIONS DERIVED FROM SELF-SIMILAR RANDOM SETS

@inproceedings{Pitman1996RANDOMDD,
  title={RANDOM DISCRETE DISTRIBUTIONS DERIVED FROM SELF-SIMILAR RANDOM SETS},
  author={Jim Pitman},
  year={1996}
}
A model is proposed for a decreasing sequence of random variables (V 1 , V 2 , · · ·) with n V n = 1, which generalizes the Poisson-Dirichlet distribution and the distribution of ranked lengths of excursions of a Brow-nian motion or recurrent Bessel process. Let V n be the length of the nth longest component interval of [0, 1]\Z, where Z is an a.s. non-empty random closed of (0, ∞) of Lebesgue measure 0, and Z is self-similar, i.e. cZ has the same distribution as Z for every c > 0. Then for 0… CONTINUE READING
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