Functional limit theorems for generalized variations of the fractional Brownian sheet
Réveillac, Anthony; Pakkanen, Mikko S. (2016), Functional limit theorems for generalized variations of the fractional Brownian sheet, Bernoulli, 22, 3, p. 1671-1708. 10.3150/15-BEJ707
Type
Article accepté pour publication ou publiéExternal document link
https://arxiv.org/abs/1404.2822v2Date
2016Journal name
BernoulliVolume
22Number
3Publisher
International Statistical Institute
Published in
Paris
Pages
1671-1708
Publication identifier
Metadata
Show full item recordAbstract (EN)
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.Subjects / Keywords
Fractional Brownian sheet; central limit theorem; non-central limit theorem; Hermite sheet; power variation; Malliavin calculusRelated items
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