Extreme Value Theory for Piecewise Contracting Maps with Randomly Applied Stochastic Perturbations

Davide Faranda (1, 2) , Jorge Milhazes Freitas (3) , Pierre Guiraud (4) , Sandro Vaienti (5, 6)

1 LSCE - Laboratoire des Sciences du Climat et de l'Environnement [Gif-sur-Yvette]
2 ESTIMR - Extrèmes : Statistiques, Impacts et Régionalisation
3 CMUP - Centro de Matemática - Universidade do Porto
4 CIMFAV - Centro de Investigación y Modelamiento de Fenómenos Aleatorios – Valparaíso
5 CPT - Ex E7 Systèmes dynamiques et théorie ergodique
6 CPT - Centre de Physique Théorique - UMR 7332

We consider globally invertible and piecewise contracting maps in higher dimensions and we perturb them with a particular kind of noise introduced by Lasota and Mackey. We got random transformations which are given by a stationary process: in this framework we develop an extreme value theory for a few classes of observables and we show how to get the (usual) limiting distributions together with an extremal index depending on the strength of the noise.

Domaines: Systèmes dynamiques [math.DS]

Davide Faranda, Jorge Milhazes Freitas, Pierre Guiraud, Sandro Vaienti. Extreme Value Theory for Piecewise Contracting Maps with Randomly Applied Stochastic Perturbations. Stochastics and Dynamics, 2016, 16 (3), pp.1660015. ⟨10.1142/S0219493716600157⟩. ⟨hal-01127758⟩