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Gaussian Measures in Finite and Infinite Dimensions

  • Textbook
  • © 2023

Overview

Authors:
  1. Daniel W. Stroock

    1. Department of Mathematics, Massachusetts Institute of Technology, Cambridge, USA

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  • 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 reference in a less specialized course or in research

Part of the book series: Universitext (UTX)

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Table of contents (4 chapters)

  1. Front Matter

    Pages i-xii
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  2. Characteristic Functions

    • Daniel W. Stroock
    Pages 1-17

  3. Gaussian Measures and Families

    • Daniel W. Stroock
    Pages 19-68

  4. Gaussian Measures on a Banach Space

    • Daniel W. Stroock
    Pages 69-99

  5. Further Properties and Examples of Abstract Wiener Spaces

    • Daniel W. Stroock
    Pages 101-139

  6. Back Matter

    Pages 141-144
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Keywords

About this book

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 techniques and ideas that have
applications in other contexts.

Authors and Affiliations

  • Department of Mathematics, Massachusetts Institute of Technology, Cambridge, USA

    Daniel W. Stroock

About the author

Daniel W. Stroock is Emeritus professor of mathematics at MIT. He is a respected mathematician in the areas of analysis, probability theory and stochastic processes. Prof. Stroock has had an active career in both the research and education.   From 2002 until 2006, he was the first holder of the second Simons Professorship of Mathematics.  In addition, he has held several administrative posts, some within the university and others outside.  In 1996, the AMS awarded him together with his former colleague jointly S.R.S. Varadhan the Leroy P. Steele Prize for seminal contributions to research in stochastic processes. Finally, he is a member of both the American Academy of Arts and Sciences, the National Academy of Sciences and a foreign member of the Polish Academy of Arts and Sciences.

Bibliographic Information

  • Book Title: Gaussian Measures in Finite and Infinite Dimensions

  • Authors: Daniel W. Stroock

  • Series Title: Universitext

  • DOI: https://doi.org/10.1007/978-3-031-23122-3

  • Publisher: Springer Cham

  • eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)

  • Copyright Information: The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Switzerland AG 2023

  • Softcover ISBN: 978-3-031-23121-6Published: 16 February 2023

  • eBook ISBN: 978-3-031-23122-3Published: 15 February 2023

  • Series ISSN: 0172-5939

  • Series E-ISSN: 2191-6675

  • Edition Number: 1

  • Number of Pages: XII, 144

  • Number of Illustrations: 1 b/w illustrations

  • Topics: Probability Theory and Stochastic Processes, Analysis, Geometry

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