Behavior of the Hermite sheet with respect to theHurst index

Héctor Araya and Ciprian A. Tudor

Stochastic Processes and their Applications, 2019, vol. 129, issue 7, 2582-2605

Abstract: We consider a d-parameter Hermite process with Hurst index H=(H1,..,Hd)∈12,1d and we study its limit behavior in distribution when the Hurst parameters Hi,i=1,..,d (or a part of them) converge to 12 and/or 1. The limit obtained is Gaussian (when at least one parameter tends to 12) and non-Gaussian (when at least one-parameter tends to 1 and none converges to 12).

Keywords: Wiener chaos; Hermite process; Rosenblatt process; Fractional Brownian motion; Multiple stochastic integrals; Cumulants; Self-similarity; Multiparameter stochastic processes (search for similar items in EconPapers)
Date: 2019
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DOI: 10.1016/j.spa.2018.07.017

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