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 W-alpha,W-beta with Hurst parameter (alpha, beta) is an element of (0, 1)(2). When 0 < alpha <= 1 - 1/2q or 0 < beta <= 1 - 1/2q a central limit theorem holds for the renormalized Hermite variations of order q >= 2, while for 1 - 1/2q < alpha, beta < 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).