ON THE RATE OF CONVERGENCE IN NON-CENTRAL ASYMPTOTICS
OF THE HERMITE VARIATIONS OF FRACTIONAL BROWNIAN SHEET
Abstract: The Hermite variations of the anisotropic fractional Brownian sheet enjoy similar
behaviour to that for the fractional Brownian motion: central (convergence to a normal
distribution) or non-central (convergence to a Hermite-type distribution). In this note, we
investigate the rate of convergence in the non-central case.
2000 AMS Mathematics Subject Classification: Primary: 60F05; Secondary: 60G22,
60G60, 62E20, 60H05.
Keywords and phrases: Convergence in variation, fractional Brownian sheet, multiple
stochastic integrals, limit theorems.