Behavior of the Hermite sheet with respect to theHurst index

Héctor Araya; Ciprian A. Tudor

doi:10.1016/j.spa.2018.07.017

Behavior of the Hermite sheet with respect to theHurst index

Héctor Araya
, Ciprian A. Tudor

Research output: Contribution to journal › Article › peer-review

4 Scopus citations

Abstract

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 language	English
Pages (from-to)	2582-2605
Number of pages	24
Journal	Stochastic Processes and their Applications
Volume	129
Issue number	7
DOIs	https://doi.org/10.1016/j.spa.2018.07.017
State	Published - Jul 2019
Externally published	Yes

Keywords

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

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title = "Behavior of the Hermite sheet with respect to theHurst index",

abstract = " 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).",

keywords = "Cumulants, Fractional Brownian motion, Hermite process, Multiparameter stochastic processes, Multiple stochastic integrals, Rosenblatt process, Self-similarity, Wiener chaos",

author = "H{\'e}ctor Araya and Tudor, \{Ciprian A.\}",

note = "Publisher Copyright: {\textcopyright} 2018 Elsevier B.V.",

year = "2019",

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doi = "10.1016/j.spa.2018.07.017",

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T1 - Behavior of the Hermite sheet with respect to theHurst index

AU - Araya, Héctor

AU - Tudor, Ciprian A.

PY - 2019/7

Y1 - 2019/7

N2 - 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).

AB - 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).

KW - Cumulants

KW - Fractional Brownian motion

KW - Hermite process

KW - Multiparameter stochastic processes

KW - Multiple stochastic integrals

KW - Rosenblatt process

KW - Self-similarity

KW - Wiener chaos

UR - https://www.scopus.com/pages/publications/85051738542

U2 - 10.1016/j.spa.2018.07.017

DO - 10.1016/j.spa.2018.07.017

M3 - Article

AN - SCOPUS:85051738542

SN - 0304-4149

VL - 129

SP - 2582

EP - 2605

JO - Stochastic Processes and their Applications

JF - Stochastic Processes and their Applications

IS - 7

ER -

Behavior of the Hermite sheet with respect to theHurst index

Abstract

Keywords

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