Gaussian Measures in Finite and Infinite D... | preigu

Cover: 9783031231216 | Gaussian Measures in Finite and Infinite Dimensions | Stroock | Buch

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Sprache: Englisch

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Beschreibung

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.

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.

Über den Autor

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.

Zusammenfassung

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

Inhaltsverzeichnis

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.

Details

Erscheinungsjahr:	2023
Fachbereich:	Wahrscheinlichkeitstheorie
Genre:	Mathematik , Medizin , Naturwissenschaften , Technik
Rubrik:	Naturwissenschaften & Technik
Medium:	Taschenbuch
Inhalt:	xii 144 S. 1 s/w Illustr. 144 p. 1 illus.
ISBN-13:	9783031231216
ISBN-10:	303123121X
Sprache:	Englisch
Einband:	Kartoniert / Broschiert
Autor:	Stroock, Daniel W.
Auflage:	1st edition 2023
Hersteller:	Springer International Publishing
Verantwortliche Person für die EU:	Springer Verlag GmbH, Tiergartenstr. 17, D-69121 Heidelberg, juergen.hartmann@springer.com
Maße:	235 x 155 x 9 mm
Von/Mit:	Daniel W. Stroock
Erscheinungsdatum:	16.02.2023
Gewicht:	0,276 kg

Artikel-ID: 125801362

Über den Autor

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.

Zusammenfassung

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

Inhaltsverzeichnis

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.

Details

Erscheinungsjahr:	2023
Fachbereich:	Wahrscheinlichkeitstheorie
Genre:	Mathematik , Medizin , Naturwissenschaften , Technik
Rubrik:	Naturwissenschaften & Technik
Medium:	Taschenbuch
Inhalt:	xii 144 S. 1 s/w Illustr. 144 p. 1 illus.
ISBN-13:	9783031231216
ISBN-10:	303123121X
Sprache:	Englisch
Einband:	Kartoniert / Broschiert
Autor:	Stroock, Daniel W.
Auflage:	1st edition 2023
Hersteller:	Springer International Publishing
Verantwortliche Person für die EU:	Springer Verlag GmbH, Tiergartenstr. 17, D-69121 Heidelberg, juergen.hartmann@springer.com
Maße:	235 x 155 x 9 mm
Von/Mit:	Daniel W. Stroock
Erscheinungsdatum:	16.02.2023
Gewicht:	0,276 kg

Artikel-ID: 125801362

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