The moduli of non-differentiability for Gaussian random fields with stationary increments

被引：5

作者：

Wang, Wensheng ^{[1
]}

Su, Zhonggen ^{[2
]}

Xiao, Yimin ^{[3
]}

机构：

[1] Hangzhou Dianzi Univ, Sch Econ, Hangzhou 310018, Peoples R China

[2] Zhejiang Univ, Sch Math Sci, Hangzhou 310027, Peoples R China

[3] Michigan State Univ, Dept Stat & Probabil, E Lansing, MI 48824 USA

来源：

BERNOULLI | 2020年 / 26卷 / 02期

关键词：

Cauchy class; fractional Riesz-Bessel process; Gaussian random field; local time; modulus of non-differentiability; strong local nondeterministism; SMALL BALL PROBABILITIES; LONG-RANGE DEPENDENCE; HOLDER CONDITIONS; HAUSDORFF MEASURE; SAMPLE FUNCTIONS; LOCAL-TIMES; INEQUALITIES; DIMENSION; EXISTENCE; MODELS;

D O I：

10.3150/19-BEJ1162

中图分类号：

O21 [概率论与数理统计]; C8 [统计学];

学科分类号：

020208 ; 070103 ; 0714 ;

摘要：

We establish the exact moduli of non-differentiability of Gaussian random fields with stationary increments. As an application of the result, we prove that the uniform Holder condition for the maximum local times of Gaussian random fields with stationary increments obtained in Xiao (1997) is optimal. These results are applicable to fractional Riesz-Bessel processes and stationary Gaussian random fields in the Matern and Cauchy classes.

引用

页码：1410 / 1430

页数：21

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