Fractal behavior of multivariate operator-self-similar stable random fields

Abstract

We investigate the sample path regularity of multivariate operator-self-similar stable random fields with values in ${\mathbb{R}}^m$ given by a harmonizable representation. Such fields were introduced in [25] as a generalization of both operator-self-similar stochastic processes and operator scaling random fields and satisfy the scaling property $\{X(c^{E}t):t\in {\mathbb{R}}^d\}\stackrel{\mathrm{d}}{=}\{c^{D}X(t):t\in {\mathbb{R}}^d\}$, where $E$ is a real $d\times d$ matrix and $D$ is a real $m\times m$ matrix. This paper provides the first results concerning sample path properties of such fields, including both $E$ and $D$ different from identity matrices. In particular, this solves an open problem in [25].

References in corpus (1)

• The Hausdorff dimension of multivariate operator-self-similar Gaussian random fields

Cited by in corpus (1)

• Sample path properties of generalized random sheets with operator scaling