Yujuan Bao, I. N. Bozkurt, T. Dayar, Xiaobai Sun, Kishor S. Trivedi
This contribution proposes a decompositional iterative method with low memory requirements for the steady-state analysis of Kronecker structured Markov chains. The Markovian system is formed by a composition of subsystems using the Kronecker sum operator for local transitions and the Kronecker product operator for synchronized transitions. Even though the interactions among subsystems, which are captured by synchronized transitions, need not be weak, numerical experiments indicate that the solver benefits considerably from weak interactions among subsystems, and is to be recommended specifically in this case.
{"title":"Decompositional Analysis of Kronecker Structured Markov Chains","authors":"Yujuan Bao, I. N. Bozkurt, T. Dayar, Xiaobai Sun, Kishor S. Trivedi","doi":"10.5072/ZENODO.47488","DOIUrl":"https://doi.org/10.5072/ZENODO.47488","url":null,"abstract":"This contribution proposes a decompositional iterative method with low memory requirements for the steady-state analysis of Kronecker structured Markov chains. The Markovian system is formed by a composition of subsystems using the Kronecker sum operator for local transitions and the Kronecker product operator for synchronized transitions. Even though the interactions among subsystems, which are captured by synchronized transitions, need not be weak, numerical experiments indicate that the solver benefits considerably from weak interactions among subsystems, and is to be recommended specifically in this case.","PeriodicalId":50536,"journal":{"name":"Electronic Transactions on Numerical Analysis","volume":null,"pages":null},"PeriodicalIF":1.3,"publicationDate":"2008-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"70792932","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2005-06-28DOI: 10.1090/S0002-9939-05-08096-2
R. Helmers, R. Zitikis
We consider generalized absolute Lorenz curves that include, as special cases, classical and generalized L-statistics as well as absolute or, in other words, generalized Lorenz curves. The curves are based on strictly stationary and ergodie sequences of random variables. Most of the previous results were obtained under the additional assumption that the sequences are weakly Bernoullian or, in other words, absolutely regular. We also argue that the latter assumption can be undesirable from the applications point of view.
{"title":"Strong laws for generalized absolute Lorenz curves when data are stationary and ergodic sequences","authors":"R. Helmers, R. Zitikis","doi":"10.1090/S0002-9939-05-08096-2","DOIUrl":"https://doi.org/10.1090/S0002-9939-05-08096-2","url":null,"abstract":"We consider generalized absolute Lorenz curves that include, as special cases, classical and generalized L-statistics as well as absolute or, in other words, generalized Lorenz curves. The curves are based on strictly stationary and ergodie sequences of random variables. Most of the previous results were obtained under the additional assumption that the sequences are weakly Bernoullian or, in other words, absolutely regular. We also argue that the latter assumption can be undesirable from the applications point of view.","PeriodicalId":50536,"journal":{"name":"Electronic Transactions on Numerical Analysis","volume":null,"pages":null},"PeriodicalIF":1.3,"publicationDate":"2005-06-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1090/S0002-9939-05-08096-2","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"60558013","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Equal values of binary forms at integral points","authors":"J. Evertse, K. Gyory, T. Shorey, R. Tijdeman","doi":"10.4064/AA-48-4-379-396","DOIUrl":"https://doi.org/10.4064/AA-48-4-379-396","url":null,"abstract":"","PeriodicalId":50536,"journal":{"name":"Electronic Transactions on Numerical Analysis","volume":null,"pages":null},"PeriodicalIF":1.3,"publicationDate":"1987-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"70479050","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"On equations in two $S$-units over function fields of characteristic $0$","authors":"J. Evertse","doi":"10.4064/AA-47-3-233-253","DOIUrl":"https://doi.org/10.4064/AA-47-3-233-253","url":null,"abstract":"","PeriodicalId":50536,"journal":{"name":"Electronic Transactions on Numerical Analysis","volume":null,"pages":null},"PeriodicalIF":1.3,"publicationDate":"1986-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"70477433","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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