Department of Economics and Business Economics

Functional limit theorems for generalized variations of the fractional Brownian sheet

Research output: Contribution to journal/Conference contribution in journal/Contribution to newspaperJournal articleResearchpeer-review

Standard

Functional limit theorems for generalized variations of the fractional Brownian sheet. / Pakkanen, Mikko; Réveillac, Anthony.

In: Bernoulli, Vol. 22, No. 3, 2016, p. 1671-1708.

Research output: Contribution to journal/Conference contribution in journal/Contribution to newspaperJournal articleResearchpeer-review

Harvard

APA

CBE

MLA

Vancouver

Author

Pakkanen, Mikko ; Réveillac, Anthony. / Functional limit theorems for generalized variations of the fractional Brownian sheet. In: Bernoulli. 2016 ; Vol. 22, No. 3. pp. 1671-1708.

Bibtex

@article{182a8e2bd02546c2beeffd3f56d19336,
title = "Functional limit theorems for generalized variations of the fractional Brownian sheet",
abstract = "We prove functional central and non-central limit theorems for generalized variations of the anisotropic d-parameter fractional Brownian sheet (fBs) for any natural number d. Whether the central or the non-central limit theorem applies depends on the Hermite rank of the variation functional and on the smallest component of the Hurst parameter vector of the fBs. The limiting process in the former result is another fBs, independent of the original fBs, whereas the limit given by the latter result is an Hermite sheet, which is driven by the same white noise as the original fBs. As an application, we derive functional limit theorems for power variations of the fBs and discuss what is a proper way to interpolate them to ensure functional convergence.",
keywords = "Fractional Brownian sheet, central limit theorem, non-central limit theorem, Hermite sheet, power variation, Malliavin calculus, Fractional Brownian sheet, Central limit theorem, Non-central limit theorem, Hermite sheet, Power variation, Malliavin calculus",
author = "Mikko Pakkanen and Anthony R{\'e}veillac",
year = "2016",
doi = "10.3150/15-BEJ707",
language = "English",
volume = "22",
pages = "1671--1708",
journal = "Bernoulli",
issn = "1350-7265",
publisher = "International Statistical Institute",
number = "3",

}

RIS

TY - JOUR

T1 - Functional limit theorems for generalized variations of the fractional Brownian sheet

AU - Pakkanen, Mikko

AU - Réveillac, Anthony

PY - 2016

Y1 - 2016

N2 - We prove functional central and non-central limit theorems for generalized variations of the anisotropic d-parameter fractional Brownian sheet (fBs) for any natural number d. Whether the central or the non-central limit theorem applies depends on the Hermite rank of the variation functional and on the smallest component of the Hurst parameter vector of the fBs. The limiting process in the former result is another fBs, independent of the original fBs, whereas the limit given by the latter result is an Hermite sheet, which is driven by the same white noise as the original fBs. As an application, we derive functional limit theorems for power variations of the fBs and discuss what is a proper way to interpolate them to ensure functional convergence.

AB - We prove functional central and non-central limit theorems for generalized variations of the anisotropic d-parameter fractional Brownian sheet (fBs) for any natural number d. Whether the central or the non-central limit theorem applies depends on the Hermite rank of the variation functional and on the smallest component of the Hurst parameter vector of the fBs. The limiting process in the former result is another fBs, independent of the original fBs, whereas the limit given by the latter result is an Hermite sheet, which is driven by the same white noise as the original fBs. As an application, we derive functional limit theorems for power variations of the fBs and discuss what is a proper way to interpolate them to ensure functional convergence.

KW - Fractional Brownian sheet, central limit theorem, non-central limit theorem, Hermite sheet, power variation, Malliavin calculus

KW - Fractional Brownian sheet

KW - Central limit theorem

KW - Non-central limit theorem

KW - Hermite sheet

KW - Power variation

KW - Malliavin calculus

U2 - 10.3150/15-BEJ707

DO - 10.3150/15-BEJ707

M3 - Journal article

VL - 22

SP - 1671

EP - 1708

JO - Bernoulli

JF - Bernoulli

SN - 1350-7265

IS - 3

ER -