Gaussian Measures in Finite and Infinite Dimensions

Daniel W. Stroock (Autor)

Buch | Softcover

XII, 144 Seiten

2023 | 1st ed. 2023
Springer International Publishing (Verlag)
978-3-031-23121-6 (ISBN)

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This text provides a concise introduction, suitable for a one-semester special topicscourse, to the remarkable properties of Gaussian measures on both finite and infinitedimensional spaces. It begins with a brief resumé of probabilistic results in which Fourieranalysis plays an essential role, and those results are then applied to derive a few basicfacts about Gaussian measures on finite dimensional spaces. In anticipation of the analysisof Gaussian measures on infinite dimensional spaces, particular attention is given to thoseproperties of Gaussian measures that are dimension independent, and Gaussian processesare constructed. The rest of the book is devoted to the study of Gaussian measures onBanach spaces. The perspective adopted is the one introduced by I. Segal and developedby L. Gross in which the Hilbert structure underlying the measure is emphasized.The contents of this bookshould be accessible to either undergraduate or graduatestudents who are interested in probability theory and have a solid background in Lebesgueintegration theory and a familiarity with basic functional analysis. Although the focus ison Gaussian measures, the book introduces its readers to techniques and ideas that haveapplications in other contexts.

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.

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.

Erscheinungsdatum	22.02.2023
Reihe/Serie	Universitext
Zusatzinfo	XII, 144 p. 1 illus.
Verlagsort	Cham
Sprache	englisch
Maße	155 x 235 mm
Gewicht	278 g
Themenwelt	Mathematik / Informatik ► Mathematik ► Analysis
	Mathematik / Informatik ► Mathematik ► Geometrie / Topologie
	Mathematik / Informatik ► Mathematik ► Wahrscheinlichkeit / Kombinatorik
Schlagworte	Banach space • Characteristic Functions • Cramer-Levy theorem • Gaussian families • Gaussian measures • Gaussian spectral properties • Gross logarithmic inequalities • Wiener spaces
ISBN-10	3-031-23121-X / 303123121X
ISBN-13	978-3-031-23121-6 / 9783031231216
Zustand	Neuware