Sample path properties of generalized random sheets with operator scaling

Abstract

We consider operator scaling $\alpha$-stable random sheets, which were introduced in [12]. The idea behind such fields is to combine the properties of operator scaling $\alpha$-stable random fields introduced in [6] and fractional Brownian sheets introduced in [14]. We establish a general uniform modulus of continuity of such fields in terms of the polar coordinates introduced [6]. Based on this, we determine the box-counting dimension and the Hausdorff dimension of the graph of a trajectory of such fields over a non-degenerate cube $I\subset Rd$.

References in corpus (4)

• Exact moduli of continuity for operator-scaling Gaussian random fields
• Modulus of continuity of some conditionally sub-Gaussian fields, application to stable random fields
• The Hausdorff dimension of multivariate operator-self-similar Gaussian random fields
• Fractal behavior of multivariate operator-self-similar stable random fields