An Introduction to the Theory of Large Deviations

  • D. W. Stroock

Part of the Universitext book series (UTX)

Table of contents

  1. Front Matter
    Pages i-vii
  2. D. W. Stroock
    Pages 1-2
  3. D. W. Stroock
    Pages 23-29
  4. D. W. Stroock
    Pages 30-75
  5. D. W. Stroock
    Pages 75-101
  6. D. W. Stroock
    Pages 114-131
  7. D. W. Stroock
    Pages 131-155
  8. D. W. Stroock
    Pages 155-179
  9. D. W. Stroock
    Pages 179-195
  10. Back Matter
    Pages 196-196

About this book

Introduction

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).

Keywords

Brownian motion Deviations Excel Grosse Abweichung Large attribute boundary element method form identification language logarithm mathematics organization set theorem

Authors and affiliations

  • D. W. Stroock
    • 1
  1. 1.Department of MathematicsMassachusetts Institute of TechnologyCambridgeUSA

Bibliographic information

  • DOI https://doi.org/10.1007/978-1-4613-8514-1
  • Copyright Information Springer-Verlag New York 1984
  • Publisher Name Springer, New York, NY
  • eBook Packages Springer Book Archive
  • Print ISBN 978-0-387-96021-0
  • Online ISBN 978-1-4613-8514-1
  • Series Print ISSN 0172-5939
  • Series Online ISSN 2191-6675
  • About this book