Speed of convergence for laws of rare events and escape rates

STOCHASTIC PROCESSES AND THEIR APPLICATIONS

卷:125

Article

Moreira Freitas, Ana Cristina^1,2  Freitas, Jorge Milhazes^3,4  Todd, Mike⁵ 

[1] Univ Porto, Ctr Matemat, P-4200464 Oporto, Portugal

[2] Univ Porto, Fac Econ, P-4200464 Oporto, Portugal

[3] Univ Porto, Ctr Matemat, P-4169007 Oporto, Portugal

[4] Univ Porto, Fac Ciencias, P-4169007 Oporto, Portugal

[5] Univ St Andrews, Math Inst, St Andrews KY16 9SS, Fife, Scotland

关键词: Extreme value theory;    Return time statistics;    Stationary stochastic processes;    Metastability;   

DOI  :  10.1016/j.spa.2014.11.011

来源: Elsevier

【 摘 要 】

We obtain error terms on the rate of convergence to Extreme Value Laws, and to the asymptotic Hitting Time Statistics, for a general class of weakly dependent stochastic processes. The dependence of the error terms on the 'time' and 'length' scales is very explicit. Specialising to data derived from a class of dynamical systems we find even more detailed error terms, one application of which is to consider escape rates through small holes in these systems. (C) 2014 Elsevier B.V. All rights reserved.

【 授权许可】

Free