Gaussian Measures in Finite and Infinite Dimensions (Universitext) - Tapa blanda

Stroock, Daniel W.

 
9783031231216: Gaussian Measures in Finite and Infinite Dimensions (Universitext)
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ISBN 10: 303123121X ISBN 13: 9783031231216
Editorial: Springer-Verlag GmbH, 2023

Sinopsis

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.

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Acerca del 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.

De la contraportada

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.

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Editorial
Springer-Verlag GmbH
Año de publicación
2023
Idioma
Inglés
ISBN 10 
303123121X
ISBN 13 
9783031231216
Encuadernación
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Número de edición
1
Número de páginas
156
Contacto del fabricante
no disponible
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Otras ediciones populares con el mismo título

9783031231230: Gaussian Measures in Finite and Infinite Dimensions

Edición Destacada

ISBN 10:  3031231236 ISBN 13:  9783031231230
Editorial: Springer, 2023
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