PERSISTENCE OF GAUSSIAN STATIONARY PROCESSES: A SPECTRAL PERSPECTIVE

• 成果类型: Article
• 署名作者: Feldheim, Naomi; Feldheim, Ohad; Nitzan, Shahaf
• 署名单位: Bar Ilan University; Hebrew University of Jerusalem; University System of Georgia; Georgia Institute of Technology
• 刊物名称: ANNALS OF PROBABILITY
• ISSN/ISSBN: 0091-1798
• DOI: 10.1214/20-AOP1470
• 发表日期: 2021
• 页码: 1067-1096
• 关键词: random polynomials; probabilities; inequalities

摘要

We study the persistence probability of a centered stationary Gaussian process on Z or R, that is, its probability to remain positive for a long time. We describe the delicate interplay between this probability and the behavior of the spectral measure of the process near zero and infinity.