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Lectures on Gaussian Processes

  • Book
  • © 2012

Overview

Authors:
  1. Mikhail Lifshits

    1. Department of Mathematics, and Mechanics, St. Petersburg State University, Stary Peterhof, Russia

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  • A quick and condensed treatment of the core theory
  • Includes supplementary material: sn.pub/extras

Part of the book series: SpringerBriefs in Mathematics (BRIEFSMATH)

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Table of contents (1 chapter)

  1. Front Matter

    Pages i-x
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  2. Lectures on Gaussian Processes

    • Mikhail Lifshits
    Pages 1-117

  3. Back Matter

    Pages 119-121
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Keywords

About this book

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.​

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)

Authors and Affiliations

  • Department of Mathematics, and Mechanics, St. Petersburg State University, Stary Peterhof, Russia

    Mikhail Lifshits

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