Open Access
February 2011 Rice formulae and Gaussian waves
Jean-Marc Azaïs, José R. León, Mario Wschebor
Bernoulli 17(1): 170-193 (February 2011). DOI: 10.3150/10-BEJ265


We use Rice formulae in order to compute the moments of some level functionals which are linked to problems in oceanography and optics: the number of specular points in one and two dimensions, the distribution of the normal angle of level curves and the number of dislocations in random wavefronts. We compute expectations and, in some cases, also second moments of such functionals. Moments of order greater than one are more involved, but one needs them whenever one wants to perform statistical inference on some parameters in the model or to test the model itself. In some cases, we are able to use these computations to obtain a central limit theorem.


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Jean-Marc Azaïs. José R. León. Mario Wschebor. "Rice formulae and Gaussian waves." Bernoulli 17 (1) 170 - 193, February 2011.


Published: February 2011
First available in Project Euclid: 8 February 2011

zbMATH: 1284.60083
MathSciNet: MR2797987
Digital Object Identifier: 10.3150/10-BEJ265

Keywords: dislocations of wavefronts , random seas , Rice formulae , specular points

Rights: Copyright © 2011 Bernoulli Society for Mathematical Statistics and Probability

Vol.17 • No. 1 • February 2011
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