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 Carbon Footprint and the Industrial Life Cycle by Péter Major
Cover of the book The Storied Nature of Human Life by Péter Major
Cover of the book Further Advances in Pragmatics and Philosophy by Péter Major
Cover of the book RuPaul’s Drag Race and the Shifting Visibility of Drag Culture by Péter Major
Cover of the book Low-Noise Low-Power Design for Phase-Locked Loops by Péter Major
Cover of the book Noise-Shaping All-Digital Phase-Locked Loops by Péter Major
Cover of the book African Democratic Citizenship Education Revisited by Péter Major
Cover of the book Berkovich Spaces and Applications by Péter Major
Cover of the book Quantum Information Processing with Finite Resources by Péter Major
Cover of the book Intercultural Competence in Organizations by Péter Major
Cover of the book Setup Planning for Machining by Péter Major
Cover of the book 2nd Karl Schwarzschild Meeting on Gravitational Physics by Péter Major
Cover of the book Unifying Theories of Programming by Péter Major
Cover of the book On Being Reformed by Péter Major
Cover of the book Dependent Growth: Foreign Investment and the Development of the Automotive Industry in East-Central Europe 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