Pier Luigi Novi Inverardi , Aldo Tagliani , Mariyan Milev
{"title":"不确定汉堡矩问题：熵收敛","authors":"Pier Luigi Novi Inverardi , Aldo Tagliani , Mariyan Milev","doi":"10.1016/j.spl.2024.110155","DOIUrl":null,"url":null,"abstract":"<div><p>The indeterminate Hamburger moment problem is considered, jointly with all its real axis supported probability density functions. As a consequence of entropy functional concavity, out of such densities there is one which has largest entropy and that plays a fundamental role: we call it <span><math><msub><mrow><mi>f</mi></mrow><mrow><mi>h</mi><mi>m</mi><mi>a</mi><mi>x</mi></mrow></msub></math></span>. It is proved that the approximate Maximum Entropy (MaxEnt) densities constrained by an increasing number of moments converge in entropy to <span><math><msub><mrow><mi>f</mi></mrow><mrow><mi>h</mi><mi>m</mi><mi>a</mi><mi>x</mi></mrow></msub></math></span> where the value of its entropy can be finite or <span><math><mrow><mo>−</mo><mi>∞</mi></mrow></math></span>.</p></div>","PeriodicalId":0,"journal":{"name":"","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2024-05-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Indeterminate Hamburger moment problem: Entropy convergence\",\"authors\":\"Pier Luigi Novi Inverardi , Aldo Tagliani , Mariyan Milev\",\"doi\":\"10.1016/j.spl.2024.110155\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<div><p>The indeterminate Hamburger moment problem is considered, jointly with all its real axis supported probability density functions. As a consequence of entropy functional concavity, out of such densities there is one which has largest entropy and that plays a fundamental role: we call it <span><math><msub><mrow><mi>f</mi></mrow><mrow><mi>h</mi><mi>m</mi><mi>a</mi><mi>x</mi></mrow></msub></math></span>. It is proved that the approximate Maximum Entropy (MaxEnt) densities constrained by an increasing number of moments converge in entropy to <span><math><msub><mrow><mi>f</mi></mrow><mrow><mi>h</mi><mi>m</mi><mi>a</mi><mi>x</mi></mrow></msub></math></span> where the value of its entropy can be finite or <span><math><mrow><mo>−</mo><mi>∞</mi></mrow></math></span>.</p></div>\",\"PeriodicalId\":0,\"journal\":{\"name\":\"\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":0.0,\"publicationDate\":\"2024-05-17\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://www.sciencedirect.com/science/article/pii/S016771522400124X\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"","FirstCategoryId":"100","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S016771522400124X","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
Indeterminate Hamburger moment problem: Entropy convergence
The indeterminate Hamburger moment problem is considered, jointly with all its real axis supported probability density functions. As a consequence of entropy functional concavity, out of such densities there is one which has largest entropy and that plays a fundamental role: we call it . It is proved that the approximate Maximum Entropy (MaxEnt) densities constrained by an increasing number of moments converge in entropy to where the value of its entropy can be finite or .
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