Multiple Wiener-Itô Integrals

Péter Major

ISBN 10: 3319026410 / ISBN 13: 9783319026411

Published by Springer International Publishing, Springer International Publishing Dez 2013, 2013

About this Item

Neuware -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 carryingout heuristic arguments.Springer Verlag GmbH, Tiergartenstr. 17, 69121 Heidelberg 144 pp. Englisch.

Seller Inventory # 9783319026411

Bibliographic Details

• Title: Multiple Wiener-Itô Integrals
• Publisher: Springer International Publishing, Springer International Publishing Dez 2013
• Publication Date: 2013
• Language: English
• ISBN 10: 3319026410
• ISBN 13: 9783319026411
• Binding: Taschenbuch
• Edition: 2nd Edition
• Condition: Neu

About this title

Synopsis

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.