PERSISTENCE PROBABILITIES IN CENTERED, STATIONARY, GAUSSIAN PROCESSES IN DISCRETE TIME

被引：4

作者：

Krishna, M. ^{[1
]}

Krishnapur, Manjunath ^{[2
]}

机构：

[1] Inst Math Sci, Madras 600113, Tamil Nadu, India

[2] Indian Inst Sci, Dept Math, Bangalore 560012, Karnataka, India

来源：

INDIAN JOURNAL OF PURE & APPLIED MATHEMATICS | 2016年 / 47卷 / 02期

关键词：

Persistence probability; hole probability; gap probability; stationary Gaussian process; spectral measure; RANDOM POLYNOMIALS; CROSSINGS; ZEROS;

D O I：

10.1007/s13226-016-0183-6

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

Lower bounds for persistence probabilities of stationary Gaussian processes in discrete time are obtained under various conditions on the spectral measure of the process. Examples are given to show that the persistence probability can decay faster than exponentially. It is shown that if the spectral measure is not singular, then the exponent in the persistence probability cannot grow faster than quadratically. An example that appears (from numerical evidence) to achieve this lower bound is presented.

引用

页码：183 / 194

页数：12

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