Behavior of the Hermite sheet with respect to the Hurst index

STOCHASTIC PROCESSES AND THEIR APPLICATIONS

卷:129

Article

Araya, Hector¹  Tudor, Ciprian A.^2,3 

[1] Univ Valparaiso, Fac Ingn, CIMFAV, Casilla 123-V, Valparaiso 4059, Chile

[2] Univ Lille 1, Lab Paul Painleve, F-59655 Villeneuve, France

[3] Romanian Acad, ISMMA, Bucharest, Romania

关键词: Wiener chaos;    Hermite process;    Rosenblatt process;    Fractional Brownian motion;    Multiple stochastic integrals;    Cumulants;    Self-similarity;    Multiparameter stochastic processes;   

DOI  :  10.1016/j.spa.2018.07.017

来源: Elsevier

【 摘 要 】

We consider a d-parameter Hermite process with Hurst index H = (H-1, . . , H-d) is an element of (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). (C) 2018 Elsevier B.V. All rights reserved.

【 授权许可】

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