{"title":"The harmonic mean formula for random processes","authors":"Krzysztof Bisewski, E. Hashorva, G. Shevchenko","doi":"10.1080/07362994.2022.2055574","DOIUrl":null,"url":null,"abstract":"Abstract Motivated by the classical harmonic mean formula, estabished by Aldous in 1989, we investigate the relation between the sojourn time and supremum of a random process and extend the harmonic mean formula for general stochastically continuous X. We discuss two applications concerning the continuity of distribution of supremum of X and representations of classical Pickands constants.","PeriodicalId":49474,"journal":{"name":"Stochastic Analysis and Applications","volume":"41 1","pages":"591 - 603"},"PeriodicalIF":0.8000,"publicationDate":"2021-06-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"4","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Stochastic Analysis and Applications","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1080/07362994.2022.2055574","RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"MATHEMATICS, APPLIED","Score":null,"Total":0}
引用次数: 4
Abstract
Abstract Motivated by the classical harmonic mean formula, estabished by Aldous in 1989, we investigate the relation between the sojourn time and supremum of a random process and extend the harmonic mean formula for general stochastically continuous X. We discuss two applications concerning the continuity of distribution of supremum of X and representations of classical Pickands constants.
期刊介绍：
Stochastic Analysis and Applications presents the latest innovations in the field of stochastic theory and its practical applications, as well as the full range of related approaches to analyzing systems under random excitation. In addition, it is the only publication that offers the broad, detailed coverage necessary for the interfield and intrafield fertilization of new concepts and ideas, providing the scientific community with a unique and highly useful service.
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