Exact moduli of continuity for operator-scaling Gaussian random fields
TLDR
In this paper, the authors prove that a centered real-valued operator-scaling Gaussian random field with stationary increments satisfies a form of strong local nondeterminism and establish its exact uniform and local moduli of continuity.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 Bierme, 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.read more
Citations
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Strong local nondeterminism and exact modulus of continuity for spherical Gaussian fields
TL;DR: In this paper, sample path properties of isotropic spherical Gaussian fields on S 2 have been investigated based on the high-frequency behavior of its angular power spectrum, and the authors exploit this result to establish an exact uniform modulus of continuity for its sample paths.
Journal ArticleDOI
Modulus of continuity of some conditionally sub-Gaussian fields, application to stable random fields
Hermine Biermé,Céline Lacaux +1 more
TL;DR: Modulus of continuity and rate of convergence of series of conditionally sub-Gaussian random fields are studied to state unified results for harmonizable (multi)operator scaling stable random fields through their LePage series representation, as well as to study sample path properties of their multistable analogous.
Journal ArticleDOI
Extremes of Gaussian random fields with regularly varying dependence structure
TL;DR: In this article, the authors consider the case that 1 − σ(t) is regularly varying at t 0 and derive the exact tail asymptotics of a Gaussian random field with variance and correlation functions.
Journal ArticleDOI
The Hausdorff dimension of multivariate operator-self-similar Gaussian random fields
TL;DR: In this article, the Hausdorff dimension of the range and graph of a trajectory over the unit cube K = [ 0, 1 ] d in the Gaussian case was investigated.
Posted Content
Sample path properties of multivariate operator-self-similar stable random fields
TL;DR: In this article, the authors investigated the sample path regularity of multivariate operator-self-similar (OSS) random fields with values in R m given by a harmonizable representation.
References
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