TY - GEN A1 - Réveillac, Anthony A1 - Stauch, Michael A1 - Tudor, Ciprian T1 - Hermite variations of the fractional Brownian sheet N2 - We prove central and non-central limit theorems for the Hermite variations of the anisotropic fractional Brownian sheet $W^{\alpha, \beta}$ with Hurst parameter $(\alpha, \beta) \in (0,1)2$. When $0<\alpha \leq 1-\frac{1}{2q}$ or $0<\beta \leq 1-\frac{1}{2q}$ a central limit theorem holds for the renormalized Hermite variations of order $q\geq 2$, while for $1-\frac{1}{2q}<\alpha, \beta < 1$ 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 $(1,1)$. Y1 - 2010 UR - https://opus4.kobv.de/opus4-matheon/frontdoor/index/index/docId/723 UR - https://nbn-resolving.org/urn:nbn:de:0296-matheon-7232 ER -