Rice formulae and Gaussian waves

Details Rice formulae and Gaussian waves Rice formulae and Gaussian waves

2011-02-02

arxiv.org/abs/1102.0389v2

Bernoulli 2011, Vol. 17, No. 1, 170-193

Mathematics

Probability

Published in at http://dx.doi.org/10.3150/10-BEJ265 the Bernoulli (http://isi.cbs.nl/bernoulli/) by the International Statisti

Scientific paper

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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