{
"id": "1708.03313",
"version": "v1",
"published": "2017-08-10T17:46:58.000Z",
"updated": "2017-08-10T17:46:58.000Z",
"title": "Limit theorems for non-linear functionals of stationary Gaussian random fields",
"authors": [
"Peter Major"
],
"comment": "82 pages, 3 figures, the text of a series of lectures",
"categories": [
"math.PR"
],
"abstract": "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",
"revisions": [
{
"version": "v1",
"updated": "2017-08-10T17:46:58.000Z"
}
],
"analyses": {
"subjects": [
"60G60",
"60H05",
"60F99"
],
"keywords": [
"stationary gaussian random fields",
"non-linear functionals",
"note multiple wiener-ito integrals",
"lecture note multiple wiener-ito",
"multiple random integrals"
],
"tags": [
"lecture notes"
],
"note": {
"typesetting": "TeX",
"pages": 82,
"language": "en",
"license": "arXiv",
"status": "editable"
}
}
}