Extreme Value Laws for Dynamical Systems with Countable Extremal Sets

• Autor(a) principal: Azevedo, D
• Data de Publicação: 2017
• Outros Autores: Ana Cristina Moreira Freitas, Jorge Milhazes Freitas, Rodrigues, FB
• Tipo de documento: Artigo
• Idioma: eng
• Título da fonte: Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos)
• Texto Completo: https://hdl.handle.net/10216/111035

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 the process, which is related to the entrance in certain regions of the phase space, which correspond to neighbourhoods of the maximal set (Formula presented.), i.e.,the set of points where the observable is maximised. The main novelty here is the fact that we consider that the set (Formula presented.) may have a countable number of points, which are associated by belonging to the orbit of a certain point, and may have accumulation points. In order to prove the existence of distributional limits and study the intensity of clustering, given by the Extremal Index, we generalise the conditions previously introduced in Freitas (Adv Math 231(5): 26262665, 2012, Stoch Process Appl 125(4): 16531687, 2015). (c) 2017 Springer Science+Business Media New York