Level Sets of Random Fields and Applications: Specular Points and Wave Crests

[摘要] We apply Rice's multidimensional formulas, in a mathematically rigorousway, to several problems which appear in random sea modeling. As a first example, the probabilitydensity function of the velocity of the specular points is obtained in one or two dimensions as wellas the expectation of the number of specular points in two dimensions. We also consider, based on amultidimensional Rice formula, a curvilinear integral with respect to the level curve. It follows that itsexpected value allows defining the Palm distribution of the angle of the normal of the curve that definesthe waves crest. Finally, we give a new proof of a general multidimensional Rice formula, valid for alllevels, for a stationary and smooth enough random fieldsX:ℝd→ℝj(d>j).

[学科分类] 应用数学