Functional limit theorems for generalized variations of the fractional Brownian sheet

Mikko S. Pakkanen () and Anthony Réveillac ()
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Mikko S. Pakkanen: CREATES and Department of Economics and Business, Aarhus University, Postal: CREATES and Department of Economics and Business, Aarhus University, Fuglesangs Alle 4, 8210 Aarhus V, Denmark.
Anthony Réveillac: CEREMADE, Université Paris-Dauphine, Postal: CEREMADE, Université Paris-Dauphine, Place du Maréchal de Lattre de Tassigny, 75775 Paris Cedex 16, France

CREATES Research Papers from Department of Economics and Business Economics, Aarhus University

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 (search for similar items in EconPapers)
JEL-codes: C10 C14 (search for similar items in EconPapers)
Pages: 39
Date: 2014-04-23
New Economics Papers: this item is included in nep-ets
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Citations: View citations in EconPapers (1)

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