Department of Economics and Business Economics

Functional limit theorems for generalized variations of the fractional Brownian sheet

Research output: Working paperResearch

Standard

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

Aarhus : Institut for Økonomi, Aarhus Universitet, 2014.

Research output: Working paperResearch

Harvard

Pakkanen, M & Réveillac, A 2014 'Functional limit theorems for generalized variations of the fractional Brownian sheet' Institut for Økonomi, Aarhus Universitet, Aarhus.

APA

Pakkanen, M., & Réveillac, A. (2014). Functional limit theorems for generalized variations of the fractional Brownian sheet. Aarhus: Institut for Økonomi, Aarhus Universitet. CREATES Research Papers, No. 2014-14

CBE

Pakkanen M, Réveillac A. 2014. Functional limit theorems for generalized variations of the fractional Brownian sheet. Aarhus: Institut for Økonomi, Aarhus Universitet.

MLA

Pakkanen, Mikko and Anthony Réveillac Functional limit theorems for generalized variations of the fractional Brownian sheet. Aarhus: Institut for Økonomi, Aarhus Universitet. (CREATES Research Papers; Journal number 2014-14). 2014., 41 p.

Vancouver

Pakkanen M, Réveillac A. Functional limit theorems for generalized variations of the fractional Brownian sheet. Aarhus: Institut for Økonomi, Aarhus Universitet. 2014 Apr 23.

Author

Pakkanen, Mikko ; Réveillac, Anthony. / Functional limit theorems for generalized variations of the fractional Brownian sheet. Aarhus : Institut for Økonomi, Aarhus Universitet, 2014. (CREATES Research Papers; No. 2014-14).

Bibtex

@techreport{75ca540c67a44c97b17d429beee18862,
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 = "2014",
month = "4",
day = "23",
language = "English",
publisher = "Institut for {\O}konomi, Aarhus Universitet",
type = "WorkingPaper",
institution = "Institut for {\O}konomi, Aarhus Universitet",

}

RIS

TY - UNPB

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

AU - Pakkanen, Mikko

AU - Réveillac, Anthony

PY - 2014/4/23

Y1 - 2014/4/23

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

M3 - Working paper

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

PB - Institut for Økonomi, Aarhus Universitet

CY - Aarhus

ER -