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Lectures on Gaussian Processes Mikhail Lifshits

Lectures on Gaussian Processes By Mikhail Lifshits

Lectures on Gaussian Processes by Mikhail Lifshits


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Summary

Gaussian processes can be viewed as a far-reaching infinite-dimensional extension of classical normal random variables. 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.

Lectures on Gaussian Processes Summary

Lectures on Gaussian Processes by Mikhail Lifshits

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.

Lectures on Gaussian Processes Reviews

From the reviews:

This is a book on the modern theory of Gaussian processes. ... I would like to recommend this book to anyone interested in the most recent developments regarding Gaussian processes and wanting to learn them from one of the best specialists in the field. (Ivan Nourdin, Mathematical Reviews, December, 2013)

Table of Contents

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.

Additional information

NLS9783642249389
9783642249389
3642249388
Lectures on Gaussian Processes by Mikhail Lifshits
New
Paperback
Springer-Verlag Berlin and Heidelberg GmbH & Co. KG
2012-01-13
121
N/A
Book picture is for illustrative purposes only, actual binding, cover or edition may vary.
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