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Gaussian Measures in Finite and Infinite Dimensions de Daniel W. Stroock

Gaussian Measures in Finite and Infinite Dimensions: Universitext

Autor Daniel W. Stroock
en Limba Engleză Paperback – 16 feb 2023
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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Specificații

ISBN-13: 9783031231216
ISBN-10: 303123121X
Pagini: 144
Ilustrații: XII, 144 p. 1 illus.
Dimensiuni: 155 x 235 mm
Greutate: 0.3 kg
Ediția:1st ed. 2023
Editura: Springer International Publishing
Colecția Springer
Seria Universitext

Locul publicării:Cham, Switzerland

Cuprins

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.

Notă biografică

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.

Textul de pe ultima copertă

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.

Caracteristici

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