# From infinite urn schemes to self-similar stable processes

Abstract : We investigate the randomized Karlin model with parameter $\beta\in(0,1)$, which is based on an infinite urn scheme. It has been shown before that when the randomization is bounded, the so-called odd-occupancy process scales to a fractional Brownian motion with Hurst index $\beta/2\in(0,1/2)$. We show here that when the randomization is heavy-tailed with index $\alpha\in(0,2)$, then the odd-occupancy process scales to a $(\beta/\alpha)$-self-similar symmetric $\alpha$-stable process with stationary increments.
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Journal articles
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Cited literature [26 references]

https://hal.archives-ouvertes.fr/hal-01622790
Contributor : Olivier Durieu <>
Submitted on : Tuesday, October 24, 2017 - 4:40:25 PM
Last modification on : Friday, June 11, 2021 - 5:12:08 PM
Long-term archiving on: : Thursday, January 25, 2018 - 2:06:03 PM

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ODGSYW.pdf
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### Identifiers

• HAL Id : hal-01622790, version 1
• ARXIV : 1710.08058

### Citation

Olivier Durieu, Gennady Samorodnitsky, Yizao Wang. From infinite urn schemes to self-similar stable processes. Stochastic Processes and their Applications, Elsevier, 2020. ⟨hal-01622790⟩

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