From infinite urn schemes to self-similar stable processes

2017/10/23 by Olivier Durieu, Durieu, Olivier, Gennady Samorodnitsky +3
Mathematics · Economics, Econometrics and Finance · Physics and Astronomy · #Stochastic processes and statistical mechanics #Complex Systems and Time Series Analysis #Theoretical and Computational Physics

paper · pdf · doi:10.48550/arxiv.1710.08058

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.

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