Singularity functions for fractional processes: application to the fractional Brownian sheet (Q2490099)

The authors consider the generalized quadratic variation of the Gaussian process. It consists of the squares of second differences instead of first ones in the usual case. It is proved that suitably normalized these generalized variation converges to the nonrandom limit. These results are applied to the fractional Brownian motion and to the estimation of the parameters for the generalized Brownian sheet.