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Multiple Wiener-Itô Integrals

With Applications to Limit Theorems

  • Péter Major

Part of the Lecture Notes in Mathematics book series (LNM, volume 849)

Table of contents

  1. Front Matter
    Pages i-xiii
  2. Péter Major
    Pages 1-8
  3. Péter Major
    Pages 9-14
  4. Péter Major
    Pages 15-26
  5. Péter Major
    Pages 27-42
  6. Péter Major
    Pages 81-86
  7. Péter Major
    Pages 87-112
  8. Péter Major
    Pages 113-122
  9. Back Matter
    Pages 123-128

About this book

Introduction

The goal of this Lecture Note is to prove a new type of limit theorems for normalized sums of strongly dependent random variables that play an important role in probability theory or in statistical physics. Here non-linear functionals of stationary Gaussian fields are considered, and it is shown that the theory of Wiener–Itô integrals provides a valuable tool in their study. More precisely, a version of these random integrals is introduced that enables us to combine the technique of random integrals and Fourier analysis. The most important results of this theory are presented together with some non-trivial limit
theorems proved with their help.
This work is a new, revised version of a previous volume written with the goalof giving a better explanation of some of the details and the motivation behind the proofs. It does not contain essentially new results; it was written to give a better insight to the old ones. In particular, a more detailed explanation of generalized fields is included to show that what is at the first sight a rather formal object is actually a useful tool for carrying out heuristic arguments.


Keywords

60G18,60H05,60F99,60G10,60G15,60G60 Wiener chaos Wiener–Itô integrals diagram formula large-scale limit self-similar fields

Authors and affiliations

  • Péter Major
    • 1
  1. 1.Hungarian Academy of Sciences Alfréd Rényi Mathematical InstituteBudapestHungary

Bibliographic information

  • DOI https://doi.org/10.1007/978-3-319-02642-8
  • Copyright Information Springer International Publishing Switzerland 2014
  • Publisher Name Springer, Cham
  • eBook Packages Mathematics and Statistics
  • Print ISBN 978-3-319-02641-1
  • Online ISBN 978-3-319-02642-8
  • Series Print ISSN 0075-8434
  • Series Online ISSN 1617-9692
  • Buy this book on publisher's site