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Gaussian Measures in Finite and Infinite Dimensions

Gaussian Measures in Finite and Infinite Dimensions - Universitext

Paperback (16 Feb 2023)

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    Publisher's Synopsis

    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.

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    Book information

    ISBN: 9783031231216
    Publisher: Springer International Publishing
    Imprint: Springer
    Pub date:
    DEWEY: 519.2
    DEWEY edition: 23
    Language: English
    Number of pages: 144
    Weight: 272g
    Height: 235mm
    Width: 155mm
    Spine width: 10mm

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