Some applications of weak dependence to extreme value theory

Several attempts to model dependence structures have been provided from 50's. Especially Murray Rosenblatt introduced a notion of strong (uniform) mixing restricting notions from dynamical systems. Anyway elementary counter examples to those notions were exhibited by both Andrews and Rosenblatt in 84. A huge bibliography is available from such notions and for example Ibragimov and Rozanov introduced $\rho-$mixing and Ibragimov and Hasminski also introduced absolute regularity. A rich asymptotic theory is available in those areas and a definitive version of it is in Rio's notes (see Arxiv 2013 for and english version of his 2000's monograph), examples of mixing time series were given in Doukhan 1994. The present talk is a proposal for alternative notions fitting much better examples of time series from Doukhan and Louhichi 1999. A reasonable asymptotical theory is available and will be rapidly sketched.
Our aim was to derive applications of times series analysis and this is thus the main aim of the talk. Since this period many applications are being developed (see eg. LNS 190 from 2007. We will describe more accurately applications to extreme values theory with adapted subsampling techniques from 2011 (with Prohl and Robert) and hard resampling (with Leucht, Lang and Neumann, submitted) and extreme values theory for time series based on O'Brien notions of phantoms (with Lang and Jakubowski, submitted).