Hitting time statistics and extreme value theory

• Type: Article in International Scientific Journal
• Date: 2010

Authors

Ana Cristina M Moreira Freitas (Author) FEP; Jorge Milhazes Freitas (Author) FCUP; Mike Todd (Author) Other

Journal

Title: Probability Theory and Related Fields

Vol. 147 No. 3

Pages: 675-710

ISSN: 0178-8051

Publisher: Springer Nature

Indexing

ISI Web of Knowledge - 131 Citations

ISI Web of Science

Scopus - 141 Citations

Scientific classification

FOS: Natural sciences > Mathematics

CORDIS: Physical sciences > Mathematics > Probability theory

Other information

Authenticus ID: 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.

Language: English

Type (Professor's evaluation): Scientific

No. of pages: 36