发布求助
文献互助 智能选刊 最新文献

High dimensional probability最新文献

筛选
英文 中文
A Probabilistic Characterization of Negative Definite Functions. 负定函数的概率表征。
High dimensional probability Pub Date : 2019-01-01 Epub Date: 2019-11-27 DOI: 10.1007/978-3-030-26391-1_5
Fuchang Gao
{"title":"A Probabilistic Characterization of Negative Definite Functions.","authors":"Fuchang Gao","doi":"10.1007/978-3-030-26391-1_5","DOIUrl":"https://doi.org/10.1007/978-3-030-26391-1_5","url":null,"abstract":"<p><p>It is proved that a continuous function <i>f</i> on ℝ <sup><i>n</i></sup> is negative definite if and only if it is polynomially bounded and satisfies the inequality <math><mrow><mi>E</mi> <mi>f</mi> <mo>(</mo> <mi>X</mi> <mo>-</mo> <mi>Y</mi> <mo>)</mo> <mo>≤</mo> <mrow><mi>E</mi> <mi>f</mi> <mo>(</mo> <mi>X</mi> <mo>+</mo> <mi>Y</mi> <mo>)</mo></mrow> </mrow> </math> for all i.i.d. random vectors <i>X</i> and <i>Y</i> in ℝ <sup><i>n</i></sup> . The proof uses Fourier transforms of tempered distributions. The \"only if\" part has been proved earlier by Lifshits et al. (A probabilistic inequality related to negative definite functions.</p>","PeriodicalId":93102,"journal":{"name":"High dimensional probability","volume":"74 ","pages":"41-53"},"PeriodicalIF":0.0,"publicationDate":"2019-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.ncbi.nlm.nih.gov/pmc/articles/PMC7604715/pdf/nihms-1631559.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"38564150","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 2
0
×
引用
GB/T 7714-2015
复制
MLA
复制
APA
复制
导出至
BibTeX EndNote RefMan NoteFirst NoteExpress
×
提示
您的信息不完整，为了账户安全，请先补充。
现在去补充
×
提示
您因"违规操作"
具体请查看互助需知
我知道了
×
提示
现在去查看 取消
×
提示
确定
请完成安全验证×
相关产品
×
本文献相关产品
联系我们：info@booksci.cn Book学术提供免费学术资源搜索服务，方便国内外学者检索中英文文献。致力于提供最便捷和优质的服务体验。 Copyright © 2023 布克学术 All rights reserved.
京ICP备2023020795号-1
ghs 京公网安备 11010802042870号
Book学术文献互助
Book学术文献互助群
群 号：481959085
Book学术官方微信