Spatial Risk Measure for Max-Stable and Max-Mixture Processes

Manaf Ahmed (1, 2) , Véronique Maume-Deschamps (1, 2) , Pierre Ribereau (1, 2) , Céline Vial (1, 3, 2)

1 ICJ - Institut Camille Jordan
2 PSPM - Probabilités, statistique, physique mathématique
3 DRACULA - Multi-scale modelling of cell dynamics : application to hematopoiesis

In this paper, we consider isotropic and stationary max-stable, inverse max-stable and max-mixture processes X=(X(s))s∈R2 and the damage process DνX=|X|ν with 0<ν<1/2. We study the quantitative behaviour of a risk measure which is the variance of the average of DνX over a region A⊂R2. This kind of risk measure has already been introduced and studied for some max-stable processes in Koch [Spatial risk measures and applications to max-stable processes, Extremes 20(3) (2017), pp. 635–670].

Mots clés: max-mixture processes; spatial risk measures

Domaines: Statistiques [math.ST]; Probabilités [math.PR]

Manaf Ahmed, Véronique Maume-Deschamps, Pierre Ribereau, Céline Vial. Spatial Risk Measure for Max-Stable and Max-Mixture Processes. Stochastics: An International Journal of Probability and Stochastic Processes, 2020, 92 (7), pp.1005-1020. ⟨10.1080/17442508.2019.1687703⟩. ⟨hal-01546570v2⟩