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

Abstract

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.

arXiv comment16 pages. arXiv admin note: text overlap with arXiv:1407.0412

References in corpus (6)

• Extremal Index, Hitting Time Statistics and periodicity
• Laws of rare events for deterministic and random dynamical systems
• Speed of convergence for laws of rare events and escape rates
• Sampling local properties of attractors via Extreme Value Theory
• Piecewise contractions defined by iterated function systems
• On the Asymptotic Properties of Piecewise Contracting Maps

Cited by in corpus (2)

• Extremes and Recurrence in Dynamical Systems
• Sampling local properties of attractors via Extreme Value Theory