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Gaussian measures in finite and infi...

Stroock, Daniel W.

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Gaussian measures in finite and infinite dimensions

紀錄類型:	書目-電子資源 : Monograph/item
正題名/作者:	Gaussian measures in finite and infinite dimensions/ by Daniel W. Stroock.
作者:	Stroock, Daniel W.
出版者:	Cham :Springer International Publishing : : 2023.,
面頁冊數:	xii, 144 p. :ill., digital ;24 cm.
內容註:	Preface -- 1. Characteristic Functions -- 2. Gaussian Measures and Families -- 3. Gaussian Measures on a Banach Space -- 4. Further Properties and Examples of Abstract Wiener Spaces -- References -- Index.
Contained By:	Springer Nature eBook
標題:	Gaussian measures. -
電子資源:	https://doi.org/10.1007/978-3-031-23122-3
ISBN:	9783031231223

Gaussian measures in finite and infinite dimensions
Stroock, Daniel W.

Gaussian measures in finite and infinite dimensions[electronic resource] /by Daniel W. Stroock. - Cham :Springer International Publishing :2023. - xii, 144 p. :ill., digital ;24 cm. - Universitext,2191-6675. - Universitext..

Preface -- 1. Characteristic Functions -- 2. Gaussian Measures and Families -- 3. Gaussian Measures on a Banach Space -- 4. Further Properties and Examples of Abstract Wiener Spaces -- References -- Index.

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 book should 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.

ISBN: 9783031231223

Standard No.: 10.1007/978-3-031-23122-3doiSubjects--Topical Terms:

672950
Gaussian measures.

LC Class. No.: QA312 / .S77 2023

Dewey Class. No.: 519.2

Gaussian measures in finite and infinite dimensions
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520 $a 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 book should 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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