Laws of rare events for deterministic and random dynamical systems

Abstract

The object of this paper is twofold. From one side we study the dichotomy, in terms of the Extremal Index of the possible Extreme Value Laws, when the rare events are centred around periodic or non periodic points. Then we build a general theory of Extreme Value Laws for randomly perturbed dynamical systems. We also address, in both situations, the convergence of Rare Events Point Processes. Decay of correlations against $L^1$ observables will play a central role in our investigations.

References in corpus (2)

• The compound Poisson limit ruling periodic extreme behaviour of non-uniformly hyperbolic dynamics
• Poisson and Compound Poisson Approximations in a Nonconventional Setup

Cited by in corpus (25)

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• Speed of convergence for laws of rare events and escape rates
• Rare Events for the Manneville-Pomeau map
• Correlation dimension and phase space contraction via extreme value theory
• Extremal dichotomy for uniformly hyperbolic systems
• Critical Transitions and Perturbation Growth Directions
• Hitting time statistics for observations of dynamical systems
• Clustering of extreme events created by multiple correlated maxima
• Extreme Value Laws for dynamical systems with countable extremal sets
• Extreme Value laws for dynamical systems under observational noise
• On the computation of the extremal index for time series
• Extreme value distributions of observation recurrences
• Hitting times and periodicity in random dynamics
• Dynamical counterexamples regarding the Extremal Index and the mean of the limiting cluster size distribution
• Decay of correlations and laws of rare events for transitive random maps
• Sampling local properties of attractors via Extreme Value Theory
• Extreme Value Laws for Superstatistics
• Clustering indices and decay of correlations in non-Markovian models
• Extreme Value Theory with Spectral Techniques: application to a simple attractor
• Extreme Value Theory for Piecewise Contracting Maps with Randomly Applied Stochastic Perturbations
• Exponential Law for Random Maps on Compact Manifolds
• A trichotomy for hitting times and escape rates for a class of unimodal maps
• Stable laws for random dynamical systems
• Rigorous pointwise approximations for invariant densities of nonuniformly expanding maps
• Pseudo-Orbits, Stationary Measures and Metastability