Functional limit theorems for generalized variations of the fractional Brownian sheet

DOI10.3150/15-BEJ707zbMath1338.60099arXiv1404.2822OpenAlexW4327674112MaRDI QIDQ282556

Mikko S. Pakkanen, Anthony Réveillac

Publication date: 12 May 2016

Published in: Bernoulli (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1404.2822

zbMATH Keywords

functional limit theoremsMalliavin calculuscentral limit theoremnon-central limit theorempower variationfractional Brownian sheetHermite sheet

Mathematics Subject Classification ID

Central limit and other weak theorems (60F05) Fractional processes, including fractional Brownian motion (60G22) Stochastic calculus of variations and the Malliavin calculus (60H07) Functional limit theorems; invariance principles (60F17)

Related Items (8)

Ambit Fields: Survey and New Challenges ⋮ Limit theorems for filtered long-range dependent random fields ⋮ Necessary and sufficient conditions for limit theorems for quadratic variations of Gaussian sequences ⋮ Local scaling limits of Lévy driven fractional random fields ⋮ Asymptotic behavior for quadratic variations of non-Gaussian multiparameter Hermite random fields ⋮ Behavior of the Hermite sheet with respect to the Hurst index ⋮ Power variations for fractional type infinitely divisible random fields ⋮ Weak convergence of weighted additive functionals of long-range dependent fields

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