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Contents of PMS, Vol. 31, Fasc. 2,
pages 301 - 311
 

ON THE RATE OF CONVERGENCE IN NON-CENTRAL ASYMPTOTICS OF THE HERMITE VARIATIONS OF FRACTIONAL BROWNIAN SHEET

Jean-Christophe Breton

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.

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