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Cover: 9783642249389 | Lectures on Gaussian Processes | Mikhail Lifshits | Taschenbuch | 2012
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Lectures on Gaussian Processes
Taschenbuch von Mikhail Lifshits
Sprache: Englisch

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Beschreibung
Gaussian processes can be viewed as a far-reaching infinite-dimensional extension of classical normal random variables. Their theory presents a powerful range of tools for probabilistic modelling in various academic and technical domains such as Statistics, Forecasting, Finance, Information Transmission, Machine Learning - to mention just a few. The objective of these Briefs is to present a quick and condensed treatment of the core theory that a reader must understand in order to make his own independent contributions. The primary intended readership are PhD/Masters students and researchers working in pure or applied mathematics. The first chapters introduce essentials of the classical theory of Gaussian processes and measures with the core notions of reproducing kernel, integral representation, isoperimetric property, large deviation principle. The brevity being a priority for teaching and learning purposes, certain technical details and proofs are omitted. The later chapters touch important recent issues not sufficiently reflected in the literature, such as small deviations, expansions, and quantization of processes. In university teaching, one can build a one-semester advanced course upon these Briefs.¿
Gaussian processes can be viewed as a far-reaching infinite-dimensional extension of classical normal random variables. Their theory presents a powerful range of tools for probabilistic modelling in various academic and technical domains such as Statistics, Forecasting, Finance, Information Transmission, Machine Learning - to mention just a few. The objective of these Briefs is to present a quick and condensed treatment of the core theory that a reader must understand in order to make his own independent contributions. The primary intended readership are PhD/Masters students and researchers working in pure or applied mathematics. The first chapters introduce essentials of the classical theory of Gaussian processes and measures with the core notions of reproducing kernel, integral representation, isoperimetric property, large deviation principle. The brevity being a priority for teaching and learning purposes, certain technical details and proofs are omitted. The later chapters touch important recent issues not sufficiently reflected in the literature, such as small deviations, expansions, and quantization of processes. In university teaching, one can build a one-semester advanced course upon these Briefs.¿
Zusammenfassung

A quick and condensed treatment of the core theory

Includes supplementary material: [...]

Inhaltsverzeichnis
Preface.- 1.Gaussian Vectors and Distributions.- 2.Examples of Gaussian Vectors, Processes and Distributions.- 3.Gaussian White Noise and Integral Representations.- 4.Measurable Functionals and the Kernel.- 5.Cameron-Martin Theorem.- 6.Isoperimetric Inequality.- 7.Measure Concavity and Other Inequalities.- 8.Large Deviation Principle.- 9.Functional Law of the Iterated Logarithm.- 10.Metric Entropy and Sample Path Properties.- 11.Small Deviations.- 12.Expansions of Gaussian Vectors.- 13.Quantization of Gaussian Vectors.- 14.Invitation to Further Reading.- References. ¿
Details
Erscheinungsjahr: 2012
Fachbereich: Wahrscheinlichkeitstheorie
Genre: Mathematik
Rubrik: Naturwissenschaften & Technik
Medium: Taschenbuch
Reihe: SpringerBriefs in Mathematics
Inhalt: x
121 S.
ISBN-13: 9783642249389
ISBN-10: 3642249388
Sprache: Englisch
Herstellernummer: 80124292
Ausstattung / Beilage: Paperback
Einband: Kartoniert / Broschiert
Autor: Lifshits, Mikhail
Hersteller: Springer-Verlag GmbH
Springer Berlin Heidelberg
SpringerBriefs in Mathematics
Maße: 235 x 155 x 8 mm
Von/Mit: Mikhail Lifshits
Erscheinungsdatum: 13.01.2012
Gewicht: 0,213 kg
Artikel-ID: 106765467
Zusammenfassung

A quick and condensed treatment of the core theory

Includes supplementary material: [...]

Inhaltsverzeichnis
Preface.- 1.Gaussian Vectors and Distributions.- 2.Examples of Gaussian Vectors, Processes and Distributions.- 3.Gaussian White Noise and Integral Representations.- 4.Measurable Functionals and the Kernel.- 5.Cameron-Martin Theorem.- 6.Isoperimetric Inequality.- 7.Measure Concavity and Other Inequalities.- 8.Large Deviation Principle.- 9.Functional Law of the Iterated Logarithm.- 10.Metric Entropy and Sample Path Properties.- 11.Small Deviations.- 12.Expansions of Gaussian Vectors.- 13.Quantization of Gaussian Vectors.- 14.Invitation to Further Reading.- References. ¿
Details
Erscheinungsjahr: 2012
Fachbereich: Wahrscheinlichkeitstheorie
Genre: Mathematik
Rubrik: Naturwissenschaften & Technik
Medium: Taschenbuch
Reihe: SpringerBriefs in Mathematics
Inhalt: x
121 S.
ISBN-13: 9783642249389
ISBN-10: 3642249388
Sprache: Englisch
Herstellernummer: 80124292
Ausstattung / Beilage: Paperback
Einband: Kartoniert / Broschiert
Autor: Lifshits, Mikhail
Hersteller: Springer-Verlag GmbH
Springer Berlin Heidelberg
SpringerBriefs in Mathematics
Maße: 235 x 155 x 8 mm
Von/Mit: Mikhail Lifshits
Erscheinungsdatum: 13.01.2012
Gewicht: 0,213 kg
Artikel-ID: 106765467
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