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Title: Exceedance assessment based on functional thresholds and general spatial measures Authors:  Jose Luis Romero - University of Granada (Spain) [presenting]
Ana Esther Madrid - University of Granada (Spain)
Jose Miguel Angulo - University of Granada (Spain)
Abstract: Spatial deformation is used in different application areas, such as image analysis or environmental studies, to represent certain forms of heterogeneity which can be explained by transformation of a reference stationary random field. An extremal analysis is often associated with the study of indicators related to geometrical characteristics of excursion sets defined by threshold exceedances. Derivation of results about threshold exceedance probabilities constitutes an open field in terms of the consideration of generalized forms of thresholds, among other aspects. In particular, the spatial deformation of a flow-type random field can be viewed as the deformation of a level-type state-rescaled random field, locally in terms of the Jacobian of the transformation. This case suggests the formalization of generalized scenarios involving functional thresholds and non-Lebesgue spatial measures.