Rare events for the Manneville-Pomeau map

• Tipo: Artigo em Revista Científica Internacional
• Data: 2016

Autores

Ana Cristina Moreira Freitas (Autor) FEP; Jorge Milhazes Freitas (Autor) FCUP; Todd, M (Autor) Outra; Vaienti, S (Autor) Outra

Revista

Título: Stochastic Processes and their Applications

Vol. 126

Páginas: 3463-3479

ISSN: 0304-4149

Editora: Elsevier

Indexação

ISI Web of Knowledge - 18 Citações

Scopus - 19 Citações

Outras Informações

ID Authenticus: P-00M-55B

DOI: 10.1016/j.spa.2016.05.001

Abstract (EN): We prove a dichotomy for Manneville-Pomeau maps f : [0, 1] -> [0, 1]: given any point zeta is an element of[0, 1], either the Rare Events Point Processes (REPP), counting the number of exceedances, which correspond to entrances in balls around zeta converge in distribution to a Poisson process; or the point zeta is periodic and the REPP converge in distribution to a compound Poisson process. Our method is to use inducing techniques for all points except 0 and its preimages, extending a recent result Haydn (2014), and then to deal with the remaining points separately. The preimages of 0 are dealt with applying recent results in Aytac (2015). The point zeta = 0 is studied separately because the tangency with the identity map at this point creates too much dependence, which causes severe clustering of exceedances. The Extremal Index, which measures the intensity of clustering, is equal to 0 at zeta = 0, which ultimately leads to a degenerate limit distribution for the partial maxima of stochastic processes arising from the dynamics and for the usual normalising sequences. We prove that using adapted normalising sequences we can still obtain non-degenerate limit distributions at zeta = 0.

Idioma: Inglês

Tipo (Avaliação Docente): Científica

Nº de páginas: 17