| 书目名称 | Gaussian Measures in Finite and Infinite Dimensions | | 编辑 | Daniel W. Stroock | | 视频video | | | 概述 | Text avoid heavy technical "machinery" common in the study of stochastic processes.Rapid intro to several major areas of math, even outside of Gaussian Measure Theory.Useful in a topics course and as | | 丛书名称 | Universitext | | 图书封面 |  | | 描述 | This text provides a concise introduction, suitable for a one-semester special topics.course, to the remarkable properties of Gaussian measures on both finite and infinite.dimensional spaces. It begins with a brief resumé of probabilistic results in which Fourier.analysis plays an essential role, and those results are then applied to derive a few basic.facts about Gaussian measures on finite dimensional spaces. In anticipation of the analysis.of Gaussian measures on infinite dimensional spaces, particular attention is given to those.properties of Gaussian measures that are dimension independent, and Gaussian processes.are constructed. The rest of the book is devoted to the study of Gaussian measures on.Banach spaces. The perspective adopted is the one introduced by I. Segal and developed.by L. Gross in which the Hilbert structure underlying the measure is emphasized..The contents of this bookshould be accessible to either undergraduate or graduate.students who are interested in probability theory and have a solid background in Lebesgue.integration theory and a familiarity with basic functional analysis. Although the focus is.on Gaussian measures, the book introduces its readers to | | 出版日期 | Textbook 2023 | | 关键词 | Gaussian measures; Wiener spaces; characteristic functions; Cramer-Levy theorem; Gaussian spectral prope | | 版次 | 1 | | doi | https://doi.org/10.1007/978-3-031-23122-3 | | isbn_softcover | 978-3-031-23121-6 | | isbn_ebook | 978-3-031-23122-3Series ISSN 0172-5939 Series E-ISSN 2191-6675 | | issn_series | 0172-5939 | | copyright | The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Switzerl |
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发表于 2025-3-21 19:53:40
