Book Details
Format
Paperback / Softback
Book Series
Universitext
ISBN-10
303123121X
ISBN-13
9783031231216
Edition
1st ed. 2023
Publisher
Springer International Publishing AG
Imprint
Springer International Publishing AG
Country of Manufacture
GB
Country of Publication
GB
Publication Date
Feb 16th, 2023
Print length
144 Pages
Product Classification:
Calculus & mathematical analysisGeometryProbability & statisticsStochastics
Ksh 8,100.00
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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.
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 thoseproperties 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 graduatestudents 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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