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

IF 1.5 2区数学 Q2 STATISTICS & PROBABILITY

Bernoulli Pub Date : 2021-08-25 DOI:10.3150/22-bej1467

C. Lee, Yimin Xiao

引用次数: 3

Abstract

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.

查看原文本刊更多论文

一类各向异性高斯随机场的迭代对数的钟型律和连续的精确模

我们建立了一大类具有可调和型积分表示和强局部不确定性性质的各向异性高斯随机场的重对数Chung型律和精确的局部一致连续模。与文献中现有的结果相比，我们的结果不需要平稳增量的假设，并且为极限常数提供了更精确的上下限。该结果适用于一类由分数有色高斯噪声驱动的线性随机偏微分方程的解，包括随机热方程。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

求助全文

约1分钟内获得全文求助全文

来源期刊

Bernoulli 数学-统计学与概率论

CiteScore

3.40

自引率

0.00%

发文量

116

审稿时长

6-12 weeks

期刊介绍： BERNOULLI is the journal of the Bernoulli Society for Mathematical Statistics and Probability, issued four times per year. The journal provides a comprehensive account of important developments in the fields of statistics and probability, offering an international forum for both theoretical and applied work. BERNOULLI will publish: Papers containing original and significant research contributions: with background, mathematical derivation and discussion of the results in suitable detail and, where appropriate, with discussion of interesting applications in relation to the methodology proposed. Papers of the following two types will also be considered for publication, provided they are judged to enhance the dissemination of research: Review papers which provide an integrated critical survey of some area of probability and statistics and discuss important recent developments. Scholarly written papers on some historical significant aspect of statistics and probability.