Exact moduli of continuity for operator-scaling Gaussian random fields

Li Yuqiang; Wang Wensheng; Xiao Yimin

doi:10.3150/13-BEJ593

Exact moduli of continuity for operator-scaling Gaussian random fields

Li Yuqiang
, Wang Wensheng
, Xiao Yimin

School of Statistics

Research output: Contribution to journal › Article › peer-review

11 Scopus citations

Abstract

Let X = {X(t), t ∈ 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 τ_E associated with the scaling exponent of X. Examples are provided to illustrate the subtle changes of the regularity properties.

Original language	English
Pages (from-to)	930-956
Number of pages	27
Journal	Bernoulli
Volume	21
Issue number	2
DOIs	https://doi.org/10.3150/13-BEJ593
State	Published - 1 May 2015

Keywords

Exact modulus of continuity
Law of the iterated logarithm
Operator-scaling gaussian fields
Strong local nondeterminism

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abstract = "Let X = \{X(t), t ∈ RN\} be a centered real-valued operator-scaling Gaussian random field with stationary increments, introduced by Bierm{\'e}, 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 τE associated with the scaling exponent of X. Examples are provided to illustrate the subtle changes of the regularity properties.",

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AU - Wensheng, Wang

AU - Yimin, Xiao

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N2 - Let X = {X(t), t ∈ RN} 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 τE associated with the scaling exponent of X. Examples are provided to illustrate the subtle changes of the regularity properties.

AB - Let X = {X(t), t ∈ RN} 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 τE associated with the scaling exponent of X. Examples are provided to illustrate the subtle changes of the regularity properties.

KW - Exact modulus of continuity

KW - Law of the iterated logarithm

KW - Operator-scaling gaussian fields

KW - Strong local nondeterminism

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Exact moduli of continuity for operator-scaling Gaussian random fields

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