Propagation of singularities in the semi-fractional Brownian sheet

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