HERMITE VARIATIONS OF THE FRACTIONAL BROWNIAN SHEET.

We prove central and non-central limit theorems for the Hermite variations of the anisotropic fractional Brownian sheet Wα, β with Hurst parameter (α, β) ∈ (0, 1)2. When $0 \lt \alpha \leq 1-\frac{1}{2q}$ or $0 \lt \beta \leq 1-\frac{1}{2q}$ a central limit theorem holds for the renormalized Hermite variations of order q ≥ 2, while for $1-\frac{1}{2q} \lt \alpha, \beta \lt 1$ 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). [ABSTRACT FROM AUTHOR]