Propagation of singularities in the semi-fractional Brownian sheet

Let X be a semi-fractional Brownian sheet, that is a centred and continuous Gaussian random field with E [ X ( s , t ) X ( s ˆ , t ˆ ) ] = ( t ∧ t ˆ ) ( s α + s ˆ α − | s − s ˆ | α ) / 2 . We provide, for α ∈ ( 0 , 2 ) , an analysis of the propagation of singularities into the fractional direction of X . Here, singularities are times where the law of the iterated logarithm fails, such as fast points.