Level Hitting Probabilities and Extremal Indexes for Some Particular Dynamical Systems
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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 x → βx 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.
KeywordsRényi map Extremes Extremal index Dynamical system Scan statistics
Mathematics Subject Classification (2010)60K99 60G10
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