Level Hitting Probabilities and Extremal Indexes for Some Particular Dynamical Systems

  • George Haiman


We establish an exact formula for the distribution of the partial maximum sequence generated by the stationary process obtained by iterations of the Rényi map xβx mod 1, β = 2, 3, .... We thus obtain a simple proof of some asymptotic behaviour of the extremes and the values of the extremal index. A numerical application is presented.


Rényi map Extremes Extremal index Dynamical system Scan statistics 

Mathematics Subject Classification (2010)

60K99 60G10 


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© Springer Science+Business Media, LLC 2017

Authors and Affiliations

  1. 1.MontrougeFrance

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