Exact moduli of continuity for operator-scaling Gaussian random fields

Abstract

Let $X=\{X(t),t\in {\mathrm{R}}^N\}$ be a centered real-valued operator-scaling Gaussian random field with stationary increments, introduced by Biermé, Meerschaert and Scheffler (Stochastic Process. Appl. 117 (2007) 312-332). We prove that $X$ satisfies a form of strong local nondeterminism and establish its exact uniform and local moduli of continuity. The main results are expressed in terms of the quasi-metric ${\tau }_E$ associated with the scaling exponent of $X$. Examples are provided to illustrate the subtle changes of the regularity properties.

Published at http://dx.doi.org/10.3150/13-BEJ593 in the Bernoulli (http://isi.cbs.nl/bernoulli/) by the International Statistical Institute/Bernoulli Society (http://isi.cbs.nl/BS/bshome.htm)

References in corpus (3)

• Joint continuity of the local times of fractional Brownian sheets
• Multivariate Operator-Self-Similar Random Fields
• On a class of space-time intrinsic random functions

Cited by in corpus (4)

• The Hausdorff dimension of multivariate operator-self-similar Gaussian random fields
• Modulus of continuity of some conditionally sub-Gaussian fields, application to stable random fields
• Generalized operator-scaling random ball model
• Sample path properties of generalized random sheets with operator scaling