Hitting time statistics and extreme value theory

• Tipo: Artigo em Revista Científica Internacional
• Data: 2010

Autores

Ana Cristina M Moreira Freitas (Autor) FEP; Jorge Milhazes Freitas (Autor) FCUP; Mike Todd (Autor) Outra

Revista

Título: Probability Theory and Related Fields

Vol. 147 Nº 3

Páginas: 675-710

ISSN: 0178-8051

Editora: Springer Nature

Indexação

ISI Web of Knowledge - 131 Citações

ISI Web of Science

Scopus - 141 Citações

Classificação Científica

FOS: Ciências exactas e naturais > Matemática

CORDIS: Ciências Físicas > Matemática > Teoria das probabilidades

Outras Informações

ID Authenticus: P-003-5FS

DOI: 10.1007/s00440-009-0221-y

Abstract (EN): 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 Extreme Value Theory (distribution properties of the partial maximum of stochastic processes). This relation allows to study Hitting Time Statistics with tools from Extreme Value Theory, and vice versa. We apply these results to non-uniformly hyperbolic systems and prove that a multimodal map with an absolutely continuous invariant measure must satisfy the classical extreme value laws (with no extra condition on the speed of mixing, for example). We also give applications of our theory to higher dimensional examples, for which we also obtain classical extreme value laws and exponential hitting time statistics (for balls). We extend these ideas to the subsequent returns to asymptotically small sets, linking the Poisson statistics of both processes.

Idioma: Inglês

Tipo (Avaliação Docente): Científica

Nº de páginas: 36