A class of fractional brownian fields from branching systems and their regularity properties

In this paper, the smoothness and exact modulus of continuity of a class of fractional Brownian fields are studied. These Gaussian random fields satisfy a kind of operator-scaling property and, depending on the choice of their parameters, may share similar fractal properties as those of fractional Brownian sheets or may be smooth in some (or all) directions. It is proved that these Gaussian random fields satisfy the property of sectorial local nondeterminism which is useful for further studying their sample path properties. In addition, the link between these Gaussian random fields and the functional fluctuation limits of branching particle systems is studied.