STOCHASTICS WITH APPLICATIONS Seminar

 

PROGRAM

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Predavanja možete pratiti i online putem MITEAM stranice seminara Stohastika sa primenama:
https://miteam.mi.sanu.ac.rs/asset/n4AMxqgneB2qxFuT2

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Plan rada seminara Stohastika sa primenama za APRIL 2026.

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Četvrtak, 23.04.2026. u 11:15, Online
Bojan Basrak, Prirodno-matematički fakultet, Univerzitet u Zagrebu
STICK-BREAKING DISTRIBUTIONS AND PITMAN-YOR THEOREM
Pitman and Yor in 1992 proved that the self-normalized jumps of $\alpha$-stable subordinators, with $\alpha \in \mathrm{(0,1)}$, have identical distributions when observed over temporal or spatial intervals. This is somewhat counterintuitive because only in the latter case such an observation includes one special, incomplete jump. The result has a number of interesting implications, particularly for the behavior of Brownian excursions. Later, they showed that the interval partitions generated in this way fit within a broader family of Poisson-Dirichlet processes, which have a wide range of mathematical applications.
We give an intuitive and constructive proof of the Pitman-Yor theorem based only on the elementary properties of Poisson processes. Moreover, employing the same approach, we present a new and simple proof for the stick-breaking distribution of length biased orderings of general Poisson-Dirichlet processes, recovering the classical results of McCloskey and Perman.

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