Multiple Wiener-Itô Integrals

With Applications to Limit Theorems
2. Auflage 2014
ISBN: 978-3-319-02641-1
Verlag: Springer International Publishing

Buch, Englisch, Band 849, 126 Seiten, Paperback, Format (B × H): 155 mm x 235 mm, Gewicht: 2292 g

Reihe: Lecture Notes in Mathematics

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.

Zielgruppe

Research

Autoren/Hrsg.

Major, Péter

Fachgebiete

• Naturwissenschaften Physik Angewandte Physik Statistische Physik, Dynamische Systeme
• Mathematik | Informatik Mathematik Stochastik Wahrscheinlichkeitsrechnung
• Mathematik | Informatik Mathematik Mathematische Analysis Integralrechnungen- und -gleichungen