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Presentations at an Academic or Professional conference (2012), Stereology, Spatial Statistics and Stochastic Geometry 7th International Conference (S4G 2012)

The Tail Distributions of Functionals of Random Excursion Sets (co-author NAGEL W.)

KRATZ Marie , NAGEL W.

When a random field $(X_t, tin {mathbb R}^D)$ is thresholded on a given level $gamma$ the excursion set is given by its indicator ${bf 1}_{(gamma , infty )}(X_t)$.The purpose of this work is to study several functionals (as established in Stochastic Geometry) of these random excursion sets, as e.g. the capacity functional, as well as the tails of their distributions. It extends results obtained for the one-dimensional case by M. Kratz and coauthors (Demichel et al. (2011), Estrade et al (2001)) to the multidimensional case, mainly when D=2, with tools borrowed to EVT and to stochastic geometry. Various approaches are considered, among which approaches based on Rice type formulas (e.g. Azais and Wschebor (2009)) or on Morse formulas (Adler and Taylor (2007)).

KRATZ, M. and NAGEL, W. (2012). The Tail Distributions of Functionals of Random Excursion Sets (co-author NAGEL W.). In: Stereology, Spatial Statistics and Stochastic Geometry 7th International Conference (S4G 2012).