4 papers · 1 filter
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…
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…