Chung-type law of the iterated logarithm and exact moduli of continuity for a class of anisotropic Gaussian random fields

We establish a Chung-type law of the iterated logarithm and the exact local and uniform moduli of continuity for a large class of anisotropic Gaussian random fields with a harmonizable-type integral representation and the property of strong local nondeterminism. Compared with the existing results in...

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Bibliographic Details
Published in:arXiv.org 2021-08
Main Authors: Cheuk Yin Lee, Xiao, Yimin
Format: Article
Language:English
Subjects:
Continuity
Fields (mathematics)
Lower bounds
Partial differential equations
Random noise
Stochastic processes
Theorems
Thermodynamics
Online Access:Get full text
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Summary:We establish a Chung-type law of the iterated logarithm and the exact local and uniform moduli of continuity for a large class of anisotropic Gaussian random fields with a harmonizable-type integral representation and the property of strong local nondeterminism. Compared with the existing results in the literature, our results do not require the assumption of stationary increments and provide more precise upper and lower bounds for the limiting constants. The results are applicable to the solutions of a class of linear stochastic partial differential equations driven by a fractional-colored Gaussian noise, including the stochastic heat equation.
ISSN:2331-8422