Lecture Notes in Mathematics

Multiple Wiener-Itô Integrals

With Applications to Limit Theorems

Authors: Major, Peter

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About this book

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 goal of 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.

Table of contents (9 chapters)

Buy this book

eBook $39.99
price for USA (gross)
  • ISBN 978-3-319-02642-8
  • Digitally watermarked, DRM-free
  • Included format: EPUB, PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Softcover $49.99
price for USA
  • ISBN 978-3-319-02641-1
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
Rent the ebook  
  • Rental duration: 1 or 6 month
  • low-cost access
  • online reader with highlighting and note-making option
  • can be used across all devices
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Bibliographic Information

Bibliographic Information
Book Title
Multiple Wiener-Itô Integrals
Book Subtitle
With Applications to Limit Theorems
Authors
Series Title
Lecture Notes in Mathematics
Series Volume
849
Copyright
2014
Publisher
Springer International Publishing
Copyright Holder
Springer International Publishing Switzerland
eBook ISBN
978-3-319-02642-8
DOI
10.1007/978-3-319-02642-8
Softcover ISBN
978-3-319-02641-1
Series ISSN
0075-8434
Edition Number
2
Number of Pages
XIII, 126
Number of Illustrations and Tables
4 b/w illustrations
Topics