191 citations · 507 across the 16 of their papers we have counts for
22 papers
A functional limit theorem for a dynamical system with an observable maximised on a Cantor set
Raquel Couto, Ana Cristina Moreira Freitas, Jorge Milhazes Freitas +1
We consider heavy-tailed observables maximised on a dynamically defined Cantor set and prove convergence of the associated point processes as well as functional limit theorems. The…
Convergence to decorated Lévy processes in non-Skorohod topologies for dynamical systems
Ana Cristina Moreira Freitas, Jorge Milhazes Freitas, Ian Melbourne +1
We present a general framework for weak convergence to decorated Lévy processes in enriched spaces of càdlàg functions for vector-valued processes arising in deterministic systems.…
Enriched functional limit theorems for dynamical systems
Ana Cristina Moreira Freitas, Jorge Milhazes Freitas, Mike Todd
We prove functional limit theorems for dynamical systems in the presence of clusters of large values which, when summed and suitably normalised, get collapsed in a jump of the limi…
Point processes of non stationary sequences generated by sequential and random dynamical systems
Ana Cristina Moreira Freitas, Jorge Milhazes Freitas, Mário Magalhães +1
We give general sufficient conditions to prove the convergence of marked point processes that keep record of the occurrence of rare events and of their impact for non-autonomous dy…
Rare events for Cantor target sets
Ana Cristina Moreira Freitas, Jorge Milhazes Freitas, Fagner B. Rodrigues +1
We study the existence of limiting laws of rare events corresponding to the entrance of the orbits on certain target sets in the phase space. The limiting laws are obtained when th…
Clustering indices and decay of correlations in non-Markovian models
Miguel Abadi, Ana Cristina Moreira Freitas, Jorge Milhazes Freitas
When there is no independence, abnormal observations may have a tendency to appear in clusters instead of scattered along the time frame. Identifying clusters and estimating their…
Dynamical counterexamples regarding the Extremal Index and the mean of the limiting cluster size distribution
Miguel Abadi, Ana Cristina Moreira Freitas, Jorge Milhazes Freitas
The Extremal Index is a parameter that measures the intensity of clustering of rare events and is usually equal to the reciprocal of the mean of the limiting cluster size distribut…
Complete convergence and records for dynamically generated stochastic processes
Ana Cristina Moreira Freitas, Jorge Milhazes Freitas, Mário Magalhães
We consider empirical multi-dimensional Rare Events Point Processes that keep track both of the time occurrence of extremal observations and of their severity, for stochastic proce…
Extreme Value Laws for dynamical systems with countable extremal sets
Davide Azevedo, Ana Cristina Moreira Freitas, Jorge Milhazes Freitas +1
We consider stationary stochastic processes arising from dynamical systems by evaluating a given observable along the orbits of the system. We focus on the extremal behaviour of th…
Extremes and Recurrence in Dynamical Systems
Valerio Lucarini, Davide Faranda, Ana Cristina Moreira Freitas +6
This book provides a comprehensive introduction for the study of extreme events in the context of dynamical systems. The introduction provides a broad overview of the interdiscipli…
Extreme Value Laws for sequences of intermittent maps
Ana Cristina Moreira Freitas, Jorge Milhazes Freitas, Sandro Vaienti
We study non-stationary stochastic processes arising from sequential dynamical systems built on maps with a neutral fixed points and prove the existence of Extreme Value Laws for s…
Extreme Value Laws for non stationary processes generated by sequential and random dynamical systems
Ana Cristina Moreira Freitas, Jorge Milhazes Freitas, Sandro Vaienti
We develop and generalize the theory of extreme value for non-stationary stochastic processes, mostly by weakening the uniform mixing condition that was previously used in this set…
Convergence of Marked Point Processes of Excesses for Dynamical Systems
Ana Cristina Moreira Freitas, Jorge Milhazes Freitas, Mário Magalhães
We consider stochastic processes arising from dynamical systems simply by evaluating an observable function along the orbits of the system and study marked point processes associat…
Clustering of extreme events created by multiple correlated maxima
Davide Azevedo, Ana Cristina Moreira Freitas, Jorge Milhazes Freitas +1
We consider stochastic processes arising from dynamical systems by evaluating an observable function along the orbits of the system. The novelty is that we will consider observable…
Rare Events for the Manneville-Pomeau map
Ana Cristina Moreira Freitas, Jorge Milhazes Freitas, Mike Todd +1
We prove a dichotomy for Manneville-Pomeau maps : given any point , either the Rare Events Point Processes (REPP), counting the number of exceedances…
Extremal dichotomy for uniformly hyperbolic systems
Maria Carvalho, Ana Cristina Moreira Freitas, Jorge Milhazes Freitas +2
We consider the extreme value theory of a hyperbolic toral automorphism showing that if a Hölder observation which is a function of a Euclide…
Speed of convergence for laws of rare events and escape rates
Ana Cristina Moreira Freitas, Jorge Milhazes Freitas, Mike Todd
We obtain error terms on the rate of convergence to Extreme Value Laws for a general class of weakly dependent stochastic processes. The dependence of the error terms on the `time'…
The compound Poisson limit ruling periodic extreme behaviour of non-uniformly hyperbolic dynamics
Ana Cristina Moreira Freitas, Jorge Milhazes Freitas, Mike Todd
We prove that the distributional limit of the normalised number of returns to small neighbourhoods of periodic points of non-uniformly hyperbolic dynamical systems is compound Pois…
Extremal Index, Hitting Time Statistics and periodicity
Ana Cristina Moreira Freitas, Jorge Milhazes Freitas, Mike Todd
We give conditions to prove the existence of an Extremal Index for general stationary stochastic processes by detecting the presence of one or more underlying periodic phenomena. T…
Extreme Value Laws in Dynamical Systems for Non-smooth Observations
Ana Cristina Moreira Freitas, Jorge Milhazes Freitas, Mike Todd
We prove the equivalence between the existence of a non-trivial hitting time statistics law and Extreme Value Laws in the case of dynamical systems with measures which are not abso…
Hitting Time Statistics and Extreme Value Theory
Ana Cristina Moreira Freitas, Jorge Milhazes Freitas, Mike Todd
We consider discrete time dynamical systems and show the link between Hitting Time Statistics (the distribution of the first time points land in asymptotically small sets) and Extr…
Extreme values for Benedicks-Carleson quadratic maps
Ana Cristina Moreira Freitas, Jorge Milhazes Freitas
We consider the quadratic family of maps given by with , where is a Benedicks-Carleson parameter. For each of these chaotic dynamical systems we…