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Level Hitting Probabilities and Extremal Indexes for Some Particular Dynamical Systems

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Abstract

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.

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Authors and Affiliations

  1. 103 av. Jean Jaurès, 92120, Montrouge, France

    George Haiman

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  1. George Haiman
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Correspondence to George Haiman.

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Haiman, G. Level Hitting Probabilities and Extremal Indexes for Some Particular Dynamical Systems. Methodol Comput Appl Probab 20, 553–562 (2018). https://doi.org/10.1007/s11009-017-9573-4

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  • DOI: https://doi.org/10.1007/s11009-017-9573-4

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