HERMITE VARIATIONS OF THE FRACTIONAL BROWNIAN SHEET

Abstract

We prove central and non-central limit theorems for the Hermite variations of the anisotropic fractional Brownian sheet Wα, βwith Hurst parameter (α, β) ∈ (0, 1)2. When [Formula: see text] or [Formula: see text] a central limit theorem holds for the renormalized Hermite variations of order q ≥ 2, while for [Formula: see text] we prove that these variations satisfy a non-central limit theorem. In fact, they converge to a random variable which is the value of a two-parameter Hermite process at time (1, 1).