TY - JOUR
T1 - Behavior of the Hermite sheet with respect to theHurst index
AU - Araya, Héctor
AU - Tudor, Ciprian A.
N1 - Publisher Copyright:
© 2018 Elsevier B.V.
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 - http://www.scopus.com/inward/record.url?scp=85051738542&partnerID=8YFLogxK
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 -