An aggregated model for Karlin stable processes

TL;DR

This paper introduces an aggregated model that approximates Karlin stable processes, extending previous models to better understand their limit behaviors and differences from other urn-based models.

Contribution

It proposes a new aggregated model for Karlin stable processes, extending Enriquez's model to include processes with regularly-varying tails.

Findings

Model scales to Karlin stable processes

Characterizes limit extremes via point process convergence

Differentiates from urn-based Karlin models

Abstract

An aggregated model is proposed, of which the partial-sum process scales to the Karlin stable processes recently investigated in the literature. The limit extremes of the proposed model, when having regularly-varying tails, are characterized by the convergence of the corresponding point processes. The proposed model is an extension of an aggregated model proposed by Enriquez (2004) in order to approximate fractional Brownian motions with Hurst index $H\in(0,1/2)$, and is of a different nature of the other recently investigated Karlin models which are essentially based on infinite urn schemes.