Level sets of random fields and applications: specular points and wave crests
type: Item
instance of: scholarly article
title: Level sets of random fields and applications: specular points and wave crests
zbMATH Open document ID: 1225.60066
DOI: 10.1155/2010/621038
author: Esteban Flores
author: José R. León
published in: International Journal of Stochastic Analysis
publication date: 2010-06-29T00:00:00Z
full work available at URL: https://eudml.org/doc/233300
review text: Summary: We apply Rice's multidimensional formulas, in a mathematically rigorous way, to several problems which appear in random sea modeling. As a first example, the probability density function of the velocity of the specular points is obtained in one or two dimensions as well as the expectation of the number of specular points in two dimensions. We also consider, based on a multidimensional Rice formula, a curvilinear integral with respect to the level curve. It follows that its expected value allows defining the Palm distribution of the angle of the normal of the curve that defines the waves crest. Finally, we give a new proof of a general multidimensional Rice formula, valid for all levels, for a stationary and a smooth enough random field \(X:\mathbb R^d\rightarrow \mathbb R^j\) \((d>j)\).
Mathematics Subject Classification ID: 60G35
Mathematics Subject Classification ID: 60G15
Mathematics Subject Classification ID: 60G17
Mathematics Subject Classification ID: 60G60
zbMATH DE Number: 5728460
zbMATH Keywords: random sea modeling
zbMATH Keywords: multidimensional Rice formula
Wikidata QID: Q58651967
MaRDI profile type: Publication
OpenAlex ID: W2054560060
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description: scientific article; zbMATH DE number 5728460