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Propagation of Singularities in the Semi-Fractional Brownian Sheet

Blath, Jochen; Martin, Andreas

Preprint-Reihe des Instituts für Mathematik, Technische Universität Berlin

Let $X$ be a semi-fractional Brownian sheet, that is a centred and continuous Gaussian random field with $\mathbb E [X(s,t)X(\hat{s},\hat{t}\,)] = (t\wedge \hat{t}\,) (s^\alpha + \hat{s}^\alpha-|s-\hat{s}|^\alpha)/2$. We provide, for $\alpha\in(0,2)$, 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.