From infinite urn schemes to self-similar stable processes

Olivier Durieu; Gennady Samorodnitsky; Yizao Wang

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arXiv · 1710.08058

From infinite urn schemes to self-similar stable processes

Olivier Durieu·Gennady Samorodnitsky·Yizao Wang

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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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BibTeX RIS

Olivier Durieu, Gennady Samorodnitsky, Yizao Wang. 2017-10-23. From infinite urn schemes to self-similar stable processes. https://arxiv.org/abs/1710.08058

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