ExtremesPub Date : 2021-09-20DOI: 10.1007/s10687-021-00425-3
Wang, Yizao
{"title":"Choquet random sup-measures with aggregations","authors":"Wang, Yizao","doi":"10.1007/s10687-021-00425-3","DOIUrl":"https://doi.org/10.1007/s10687-021-00425-3","url":null,"abstract":"<p>A variation of Choquet random sup-measures is introduced. These random sup-measures are shown to arise as the scaling limits of empirical random sup-measures of a general aggregated model. Because of the aggregations, the finite-dimensional distributions of introduced random sup-measures do not necessarily have classical extreme-value distributions. Examples include the recently introduced stable-regenerative random sup-measures as a special case.</p>","PeriodicalId":49274,"journal":{"name":"Extremes","volume":"19 1","pages":""},"PeriodicalIF":1.3,"publicationDate":"2021-09-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138537971","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
ExtremesPub Date : 2021-09-20DOI: 10.1007/s10687-021-00427-1
Foss, Sergey, Korshunov, Dmitry, Palmowski, Zbigniew
{"title":"Branching processes with immigration in atypical random environment","authors":"Foss, Sergey, Korshunov, Dmitry, Palmowski, Zbigniew","doi":"10.1007/s10687-021-00427-1","DOIUrl":"https://doi.org/10.1007/s10687-021-00427-1","url":null,"abstract":"<p>Motivated by a seminal paper of Kesten et al. (<i>Ann. Probab.</i>, <i>3(1)</i>, 1–31, 1975) we consider a branching process with a conditional geometric offspring distribution with i.i.d. random environmental parameters <i>A</i><sub><i>n</i></sub>, <i>n</i> ≥ 1 and with one immigrant in each generation. In contrast to above mentioned paper we assume that the environment is long-tailed, that is that the distribution <i>F</i> of <span>(xi _{n}:=log ((1-A_{n})/A_{n}))</span> is long-tailed. We prove that although the offspring distribution is light-tailed, the environment itself can produce extremely heavy tails of the distribution of the population size in the <i>n</i> th generation which becomes even heavier with increase of <i>n</i>. More precisely, we prove that, for all <i>n</i>, the distribution tail <span>(mathbb {P}(Z_{n} ge m))</span> of the <i>n</i> th population size <i>Z</i><sub><i>n</i></sub> is asymptotically equivalent to <span>(noverline F(log m))</span> as <i>m</i> grows. In this way we generalise Bhattacharya and Palmowski (<i>Stat. Probab. Lett.</i>, <i>154</i>, 108550, 2019) who proved this result in the case <i>n</i> = 1 for regularly varying environment <i>F</i> with parameter <i>α</i> > 1. Further, for a subcritical branching process with subexponentially distributed <i>ξ</i><sub><i>n</i></sub>, we provide the asymptotics for the distribution tail <span>(mathbb {P}(Z_{n}>m))</span> which are valid uniformly for all <i>n</i>, and also for the stationary tail distribution. Then we establish the “principle of a single atypical environment” which says that the main cause for the number of particles to be large is the presence of a single very small environmental parameter <i>A</i><sub><i>k</i></sub>.</p>","PeriodicalId":49274,"journal":{"name":"Extremes","volume":"34 1","pages":""},"PeriodicalIF":1.3,"publicationDate":"2021-09-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138537967","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
ExtremesPub Date : 2021-09-11DOI: 10.1007/s10687-021-00428-0
Mads Stehr, Anders Rønn-Nielsen
{"title":"Extremes of subexponential Lévy-driven random fields in the Gumbel domain of attraction","authors":"Mads Stehr, Anders Rønn-Nielsen","doi":"10.1007/s10687-021-00428-0","DOIUrl":"https://doi.org/10.1007/s10687-021-00428-0","url":null,"abstract":"","PeriodicalId":49274,"journal":{"name":"Extremes","volume":"25 1","pages":"79 - 105"},"PeriodicalIF":1.3,"publicationDate":"2021-09-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"52394337","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
ExtremesPub Date : 2021-09-06DOI: 10.1007/s10687-022-00442-w
G. Barrera, Paulo Manrique-Mirón
{"title":"The asymptotic distribution of the condition number for random circulant matrices","authors":"G. Barrera, Paulo Manrique-Mirón","doi":"10.1007/s10687-022-00442-w","DOIUrl":"https://doi.org/10.1007/s10687-022-00442-w","url":null,"abstract":"","PeriodicalId":49274,"journal":{"name":"Extremes","volume":"25 1","pages":"567 - 594"},"PeriodicalIF":1.3,"publicationDate":"2021-09-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43233925","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
ExtremesPub Date : 2021-08-06DOI: 10.1007/s10687-022-00439-5
Tiandong Wang, S. Resnick
{"title":"Asymptotic dependence of in- and out-degrees in a preferential attachment model with reciprocity","authors":"Tiandong Wang, S. Resnick","doi":"10.1007/s10687-022-00439-5","DOIUrl":"https://doi.org/10.1007/s10687-022-00439-5","url":null,"abstract":"","PeriodicalId":49274,"journal":{"name":"Extremes","volume":"25 1","pages":"417 - 450"},"PeriodicalIF":1.3,"publicationDate":"2021-08-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42474995","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
ExtremesPub Date : 2021-07-20DOI: 10.1007/s10687-022-00461-7
M. Kratz, E. Prokopenko
{"title":"Multi-normex distributions for the sum of random vectors. Rates of convergence","authors":"M. Kratz, E. Prokopenko","doi":"10.1007/s10687-022-00461-7","DOIUrl":"https://doi.org/10.1007/s10687-022-00461-7","url":null,"abstract":"","PeriodicalId":49274,"journal":{"name":"Extremes","volume":"1 1","pages":"1-36"},"PeriodicalIF":1.3,"publicationDate":"2021-07-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42966266","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
ExtremesPub Date : 2021-06-05DOI: 10.1007/s10687-021-00417-3
Philippe Soulier
{"title":"The tail process and tail measure of continuous time regularly varying stochastic processes","authors":"Philippe Soulier","doi":"10.1007/s10687-021-00417-3","DOIUrl":"https://doi.org/10.1007/s10687-021-00417-3","url":null,"abstract":"<p>The goal of this paper is to investigate the tools of extreme value theory originally introduced for discrete time stationary stochastic processes (time series), namely the tail process and the tail measure, in the framework of continuous time stochastic processes with paths in the space <span>(mathcal {D})</span> of càdlàg functions indexed by <span>(mathbb {R})</span>, endowed with Skorohod’s <i>J</i><sub>1</sub> topology. We prove that the essential properties of these objects are preserved, with some minor (though interesting) differences arising. We first obtain structural results which provide representation for homogeneous shift-invariant measures on <span>(mathcal {D})</span> and then study regular variation of random elements in <span>(mathcal {D})</span>. We give practical conditions and study several examples, recovering and extending known results.</p>","PeriodicalId":49274,"journal":{"name":"Extremes","volume":"39 1","pages":""},"PeriodicalIF":1.3,"publicationDate":"2021-06-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138537970","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
ExtremesPub Date : 2021-06-01DOI: 10.1007/s10687-021-00422-6
Zhendong Huang, O. Shulyarenko, Davide Ferrari
{"title":"Truncated pair-wise likelihood for the Brown-Resnick process with applications to maximum temperature data","authors":"Zhendong Huang, O. Shulyarenko, Davide Ferrari","doi":"10.1007/s10687-021-00422-6","DOIUrl":"https://doi.org/10.1007/s10687-021-00422-6","url":null,"abstract":"","PeriodicalId":49274,"journal":{"name":"Extremes","volume":"24 1","pages":"379 - 402"},"PeriodicalIF":1.3,"publicationDate":"2021-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1007/s10687-021-00422-6","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45707910","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
ExtremesPub Date : 2021-05-11DOI: 10.1007/s10687-021-00434-2
Zhongwei Zhang, Raphael Huser, T. Opitz, J. Wadsworth
{"title":"Modeling spatial extremes using normal mean-variance mixtures","authors":"Zhongwei Zhang, Raphael Huser, T. Opitz, J. Wadsworth","doi":"10.1007/s10687-021-00434-2","DOIUrl":"https://doi.org/10.1007/s10687-021-00434-2","url":null,"abstract":"","PeriodicalId":49274,"journal":{"name":"Extremes","volume":"25 1","pages":"175 - 197"},"PeriodicalIF":1.3,"publicationDate":"2021-05-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48692836","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
ExtremesPub Date : 2021-05-07DOI: 10.1007/s10687-021-00415-5
Mads Stehr, Anders Rønn-Nielsen
{"title":"Extreme value theory for spatial random fields – with application to a Lévy-driven field","authors":"Mads Stehr, Anders Rønn-Nielsen","doi":"10.1007/s10687-021-00415-5","DOIUrl":"https://doi.org/10.1007/s10687-021-00415-5","url":null,"abstract":"","PeriodicalId":49274,"journal":{"name":"Extremes","volume":"24 1","pages":"753 - 795"},"PeriodicalIF":1.3,"publicationDate":"2021-05-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1007/s10687-021-00415-5","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"41444506","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}