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 Theoretical Computer Science and Discrete Mathematics by Péter Major
Cover of the book Approximation and Online Algorithms by Péter Major
Cover of the book Building a Passive House by Péter Major
Cover of the book Sporotrichosis by Péter Major
Cover of the book Internationalism, Imperialism and the Formation of the Contemporary World by Péter Major
Cover of the book Computer Vision – ECCV 2016 by Péter Major
Cover of the book Adaptive Biometric Systems by Péter Major
Cover of the book Proceedings of the 2nd Workshop on Communication Security by Péter Major
Cover of the book Fusion of Smart, Multimedia and Computer Gaming Technologies by Péter Major
Cover of the book Dynamical Systems: Theoretical and Experimental Analysis by Péter Major
Cover of the book Advances in Nanostructured Cellulose-based Biomaterials by Péter Major
Cover of the book The Political Theology of European Integration by Péter Major
Cover of the book Cognitive Joyce by Péter Major
Cover of the book Modeling and Using Context by Péter Major
Cover of the book Insights from Research in Science Teaching and Learning 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