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An Introduction to the Theory of Large Deviations

  • Textbook
  • © 1984

Overview

Authors:
  1. D. W. Stroock

    1. Department of Mathematics, Massachusetts Institute of Technology, Cambridge, USA

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Part of the book series: Universitext (UTX)

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Table of contents (10 chapters)

  1. Front Matter

    Pages i-vii
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  2. Introduction

    • D. W. Stroock
    Pages 1-2

  3. Brownian Motion in Small Time, Strassen’s Iterated Logarithm

    • D. W. Stroock
    Pages 2-22

  4. Large Deviations, Some Generalities

    • D. W. Stroock
    Pages 23-29

  5. Cramér’s Theorem

    • D. W. Stroock
    Pages 30-75

  6. Large Deviation Principle for Diffusions

    • D. W. Stroock
    Pages 75-101

  7. Introduction to Large Deviations from Ergodic Phenomena

    • D. W. Stroock
    Pages 101-114

  8. Existence of a Rate Function

    • D. W. Stroock
    Pages 114-131

  9. Identification of the Rate Function

    • D. W. Stroock
    Pages 131-155

  10. Some Non-Uniform Large Deviation Results

    • D. W. Stroock
    Pages 155-179

  11. Logarithmic Sobolev Inequalities

    • D. W. Stroock
    Pages 179-195

  12. Back Matter

    Pages 196-196
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Keywords

About this book

These notes are based on a course which I gave during the academic year 1983-84 at the University of Colorado. My intention was to provide both my audience as well as myself with an introduction to the theory of 1arie deviations • The organization of sections 1) through 3) owes something to chance and a great deal to the excellent set of notes written by R. Azencott for the course which he gave in 1978 at Saint-Flour (cf. Springer Lecture Notes in Mathematics 774). To be more precise: it is chance that I was around N. Y. U. at the time'when M. Schilder wrote his thesis. and so it may be considered chance that I chose to use his result as a jumping off point; with only minor variations. everything else in these sections is taken from Azencott. In particular. section 3) is little more than a rewrite of his exoposition of the Cramer theory via the ideas of Bahadur and Zabel. Furthermore. the brief treatment which I have given to the Ventsel-Freidlin theory in section 4) is again based on Azencott's ideas. All in all. the biggest difference between his and my exposition of these topics is the language in which we have written. However. another major difference must be mentioned: his bibliography is extensive and constitutes a fine introduction to the available literature. mine shares neither of these attributes. Starting with section 5).

Authors and Affiliations

  • Department of Mathematics, Massachusetts Institute of Technology, Cambridge, USA

    D. W. Stroock

Bibliographic Information

  • Book Title: An Introduction to the Theory of Large Deviations

  • Authors: D. W. Stroock

  • Series Title: Universitext

  • DOI: https://doi.org/10.1007/978-1-4613-8514-1

  • Publisher: Springer New York, NY

  • eBook Packages: Springer Book Archive

  • Copyright Information: Springer-Verlag New York Inc. 1984

  • Softcover ISBN: 978-0-387-96021-0Published: 01 August 1984

  • eBook ISBN: 978-1-4613-8514-1Published: 06 December 2012

  • Series ISSN: 0172-5939

  • Series E-ISSN: 2191-6675

  • Edition Number: 1

  • Number of Pages: 196

  • Topics: Applications of Mathematics

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