From infinite urn schemes to self-similar stable processes

Olivier Durieu, Gennady Samorodnitsky and Yizao Wang

Stochastic Processes and their Applications, 2020, vol. 130, issue 4, 2471-2487

Abstract: We investigate the randomized Karlin model with parameter β∈(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 β∕2∈(0,1∕2). We show here that when the randomization is heavy-tailed with index α∈(0,2), then the odd-occupancy process scales to a (β∕α)-self-similar symmetric α-stable process with stationary increments.

Keywords: Infinite urn scheme; Regular variation; Functional central limit theorem; Self-similar process; Stable process (search for similar items in EconPapers)
Date: 2020
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Citations: View citations in EconPapers (2)

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DOI: 10.1016/j.spa.2019.07.008

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