02526nmm a2200385 i 4500991003325769707536cr cn ---mpcbr170207s2014 sz | o j |||| 0|eng d9783319026428 (ebook)10.1007/978-3-319-02642-8doib14316298-39ule_instBibl. Dip.le Aggr. Matematica e Fisica - Sez. Matematicaeng519.223AMS 60G15AMS 60H05Major, Péter48603Multiple Wiener-Itô Integrals[e-book] :With Applications to Limit Theorems /by Péter Major2nd ed.Cham :Springer Intern. Publ.,20141 online resourcetexttxtrdacontentcomputercrdamediaonline resourcecrrdacarriertext filePDFrdaLecture Notes in Mathematics,1617-9692 ;849The 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 goalof 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 argumentsDistribution (Probability theory)Springer eBooksPrinted edition:9783319026411http://link.springer.com/book/10.1007/978-3-319-02642-8An electronic book accessible through the World Wide.b1431629803-03-2207-02-17991003325769707536Multiple Wiener-Itô integrals81079UNISALENTOle01307-02-17m@ -engsz 00