Functional limit theorems for generalized variations of the fractional Brownian sheet - Archive ouverte HAL Access content directly
Preprints, Working Papers, ... Year : 2014

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.
Fichier principal
Vignette du fichier
Pakkanen_Reveillac.pdf (366.13 Ko) Télécharger le fichier
Origin Files produced by the author(s)
Loading...

Dates and versions

hal-00976747 , version 1 (10-04-2014)

Identifiers

Cite

Mikko S. Pakkanen, Anthony Réveillac. Functional limit theorems for generalized variations of the fractional Brownian sheet. 2014. ⟨hal-00976747⟩
123 View
102 Download

Altmetric

Share

Gmail Mastodon Facebook X LinkedIn More