Behavior of the Hermite sheet with respect to theHurst index

Héctor Araya, Ciprian A. Tudor

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4 Scopus citations


We consider a d-parameter Hermite process with Hurst index H=(H 1 ,.,H d )∈1/2,1 d and we study its limit behavior in distribution when the Hurst parameters H i ,i=1,.,d (or a part of them) converge to 1/2 and/or 1. The limit obtained is Gaussian (when at least one parameter tends to 1/2) and non-Gaussian (when at least one-parameter tends to 1 and none converges to 1/2).

Original languageEnglish
Pages (from-to)2582-2605
Number of pages24
JournalStochastic Processes and their Applications
Issue number7
StatePublished - Jul 2019
Externally publishedYes


  • Cumulants
  • Fractional Brownian motion
  • Hermite process
  • Multiparameter stochastic processes
  • Multiple stochastic integrals
  • Rosenblatt process
  • Self-similarity
  • Wiener chaos


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