{"title":"Extremes of locally-homogenous vector-valued Gaussian processes","authors":"Pavel Ievlev","doi":"10.1007/s10687-023-00483-9","DOIUrl":null,"url":null,"abstract":"<p>In this paper, we study the asymptotical behaviour of high exceedence probabilities for centered continuous <span>\\(\\mathbb {R}^n\\)</span>-valued Gaussian random field <span>\\(\\varvec{X}\\)</span> with covariance matrix satisfying <span>\\(\\Sigma - R ( t + s, t ) \\sim \\sum _{l = 1}^n B_l ( t ) \\, | s_l |^{\\alpha _l}\\)</span> as <span>\\(s \\downarrow 0\\)</span>. Such processes occur naturally as time transformations of homogenous random fields, and we present two asymptotic results of this nature as applications of our findings. The technical novelty of our proof consists in showing that the Slepian-Gordon inequality technique, essential in the univariate case, can also be successfully applied in the multivariate setup. This is noteworthy because this technique was previously believed to be inaccessible in this particular context.</p>","PeriodicalId":49274,"journal":{"name":"Extremes","volume":"80 1","pages":""},"PeriodicalIF":1.1000,"publicationDate":"2024-01-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Extremes","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1007/s10687-023-00483-9","RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"MATHEMATICS, INTERDISCIPLINARY APPLICATIONS","Score":null,"Total":0}
引用次数: 0
Abstract
In this paper, we study the asymptotical behaviour of high exceedence probabilities for centered continuous \(\mathbb {R}^n\)-valued Gaussian random field \(\varvec{X}\) with covariance matrix satisfying \(\Sigma - R ( t + s, t ) \sim \sum _{l = 1}^n B_l ( t ) \, | s_l |^{\alpha _l}\) as \(s \downarrow 0\). Such processes occur naturally as time transformations of homogenous random fields, and we present two asymptotic results of this nature as applications of our findings. The technical novelty of our proof consists in showing that the Slepian-Gordon inequality technique, essential in the univariate case, can also be successfully applied in the multivariate setup. This is noteworthy because this technique was previously believed to be inaccessible in this particular context.
ExtremesMATHEMATICS, INTERDISCIPLINARY APPLICATIONS-STATISTICS & PROBABILITY
CiteScore
2.20
自引率
7.70%
发文量
15
审稿时长
>12 weeks
期刊介绍:
Extremes publishes original research on all aspects of statistical extreme value theory and its applications in science, engineering, economics and other fields. Authoritative and timely reviews of theoretical advances and of extreme value methods and problems in important applied areas, including detailed case studies, are welcome and will be a regular feature. All papers are refereed. Publication will be swift: in particular electronic submission and correspondence is encouraged.
Statistical extreme value methods encompass a very wide range of problems: Extreme waves, rainfall, and floods are of basic importance in oceanography and hydrology, as are high windspeeds and extreme temperatures in meteorology and catastrophic claims in insurance. The waveforms and extremes of random loads determine lifelengths in structural safety, corrosion and metal fatigue.