An aggregated model for Karlin stable processes

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 [10] in order to approximate fractional Brownian motions with Hurst index H ∈ (0, 1/2), and is of a different nature of the other recently investigated Karlin models which are essentially based on infinite urn schemes.