Multiple Wiener-Itô Integrals

With Applications to Limit Theorems

Nonfiction, Science & Nature, Mathematics, Statistics
Cover of the book Multiple Wiener-Itô Integrals by Péter Major, Springer International Publishing
View on Amazon View on AbeBooks View on Kobo View on B.Depository View on eBay View on Walmart
Author: Péter Major ISBN: 9783319026428
Publisher: Springer International Publishing Publication: December 2, 2013
Imprint: Springer Language: English
Author: Péter Major
ISBN: 9783319026428
Publisher: Springer International Publishing
Publication: December 2, 2013
Imprint: Springer
Language: English

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.

View on Amazon View on AbeBooks View on Kobo View on B.Depository View on eBay View on Walmart

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.

More books from Springer International Publishing

Cover of the book Leveraging by Péter Major
Cover of the book Atlas of Infections in Neurosurgery and Spinal Surgery by Péter Major
Cover of the book New Production Technologies in Aerospace Industry by Péter Major
Cover of the book The Frontiers of Applied Demography by Péter Major
Cover of the book Sovereign Debt by Péter Major
Cover of the book 3rd International Multidisciplinary Microscopy and Microanalysis Congress (InterM) by Péter Major
Cover of the book Critical Approaches to Welcome to Night Vale by Péter Major
Cover of the book The Science of Human Evolution by Péter Major
Cover of the book Supervisory Control of Discrete-Event Systems by Péter Major
Cover of the book Innovative Security Solutions for Information Technology and Communications by Péter Major
Cover of the book Food Bioactives by Péter Major
Cover of the book Parental Responsibility in the Context of Neuroscience and Genetics by Péter Major
Cover of the book The Dark Side of Silicon by Péter Major
Cover of the book Rethinking the Irish Diaspora by Péter Major
Cover of the book Haunting Modernisms by Péter Major
We use our own "cookies" and third party cookies to improve services and to see statistical information. By using this website, you agree to our Privacy Policy