Sojourn times of Gaussian and related random fields

IF 0.6 4区 数学 Q4 STATISTICS & PROBABILITY
K. Dȩbicki, E. Hashorva, Peng Liu, Z. Michna
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引用次数: 1

Abstract

. This paper is concerned with the asymptotic analysis of sojourn times of random fields with continuous sample paths. Under a very general framework we show that there is an interesting relationship between tail asymptotics of sojourn times and that of supremum. Moreover, we establish the uniform double-sum method to derive the tail asymptotics of sojourn times. In the literature, based on the pioneering research of S. Berman the sojourn times have been utilised to derive the tail asymptotics of supremum of Gaussian processes. In this paper we show that the opposite direction is even more fruitful, namely knowing the asymptotics of supremum of random processes and fields (in particular Gaussian) it is possible to establish the asymptotics of their sojourn times. We illustrate our findings considering i) two dimensional Gaussian random fields, ii) chi-process generated by stationary Gaussian processes and iii) stationary Gaussian queueing processes.
高斯及相关随机场的逗留时间
。本文研究了具有连续样本路径的随机场逗留时间的渐近分析。在一个非常一般的框架下,我们证明了逗留时间的尾部渐近性与上极值的尾部渐近性之间有一个有趣的关系。此外,我们建立了一致双和方法来推导逗留时间的尾部渐近性。在文献中,基于S. Berman的开创性研究,逗留时间已被用来推导高斯过程的上极值的尾部渐近性。在本文中,我们证明了相反的方向更有效,即知道随机过程和随机域(特别是高斯)的上极值的渐近性,就有可能建立它们逗留时间的渐近性。我们考虑i)二维高斯随机场,ii)平稳高斯过程产生的chi过程和iii)平稳高斯排队过程来说明我们的发现。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
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来源期刊
CiteScore
1.10
自引率
0.00%
发文量
48
期刊介绍: ALEA publishes research articles in probability theory, stochastic processes, mathematical statistics, and their applications. It publishes also review articles of subjects which developed considerably in recent years. All articles submitted go through a rigorous refereeing process by peers and are published immediately after accepted. ALEA is an electronic journal of the Latin-american probability and statistical community which provides open access to all of its content and uses only free programs. Authors are allowed to deposit their published article into their institutional repository, freely and with no embargo, as long as they acknowledge the source of the paper. ALEA is affiliated with the Institute of Mathematical Statistics.
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