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Journal Articles Stochastic Processes and their Applications Year : 2020

From infinite urn schemes to self-similar stable processes

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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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Dates and versions

hal-01622790 , version 1 (24-10-2017)

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