平稳高斯过程零个数方差的一个渐近公式。

IF 1.5 1区数学 Q2 STATISTICS & PROBABILITY Probability Theory and Related Fields Pub Date : 2023-01-01 Epub Date: 2023-09-23 DOI:10.1007/s00440-023-01218-4

Eran Assaf, Jeremiah Buckley, Naomi Feldheim

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引用次数: 6

摘要

我们研究了平稳高斯过程在长区间上零点数的方差。在温和混合条件下，我们给出了一个简单的渐近描述。这使我们能够表征最小和最大的增长。我们证明，在特定频率的光谱测量中，一个小的（对称的）原子不会影响方差的渐近增长，而在任何其他频率的原子都会导致最大增长。

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An asymptotic formula for the variance of the number of zeroes of a stationary Gaussian process.

We study the variance of the number of zeroes of a stationary Gaussian process on a long interval. We give a simple asymptotic description under mild mixing conditions. This allows us to characterise minimal and maximal growth. We show that a small (symmetrised) atom in the spectral measure at a special frequency does not affect the asymptotic growth of the variance, while an atom at any other frequency results in maximal growth.

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来源期刊

Probability Theory and Related Fields 数学-统计学与概率论

CiteScore

3.70

自引率

5.00%

发文量

审稿时长

6-12 weeks

期刊介绍： Probability Theory and Related Fields publishes research papers in modern probability theory and its various fields of application. Thus, subjects of interest include: mathematical statistical physics, mathematical statistics, mathematical biology, theoretical computer science, and applications of probability theory to other areas of mathematics such as combinatorics, analysis, ergodic theory and geometry. Survey papers on emerging areas of importance may be considered for publication. The main languages of publication are English, French and German.