### arXiv:1708.03313 [math.PR]AbstractReferencesReviewsResources

#### Limit theorems for non-linear functionals of stationary Gaussian random fields

Published 2017-08-10Version 1

This is an extended version of a series of talks I held at the University of Bochum in 2017 about limit theorems for non-linear functionals of stationary Gaussian random fields. The goal of these talks was to give a fairly detailed introduction to the theory leading to such results, even if some of the results are presented without proof. On the other hand, I gave a simpler proof for some of the results. (The proofs omitted from this text can be found in my Springer Lecture Note Multiple Wiener--Ito Integrals. In this note first I discuss the spectral representation of the covariance function of a Gaussian stationary rendom field by means of the spectral measure and the representation of the elements of the random field by means of a random integral with respect to the random spectral measure. Then I construct the multiple random integrals with respect to the random spectral measure and prove their most important properties. Finally I show some interesting applications of these multiple random integrals. In particular, I prove some non-trivial non-Gaussian limit theorems

**Comments:**82 pages, 3 figures, the text of a series of lectures

**Categories:**math.PR

**Keywords:**stationary gaussian random fields, non-linear functionals, note multiple wiener-ito integrals, lecture note multiple wiener-ito, multiple random integrals

**Tags:**lecture notes