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Level Hitting Probabilities and Extremal Indexes for Some Particular Dynamical Systems

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  • George Haiman

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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  • George Haiman, 2018. "Level Hitting Probabilities and Extremal Indexes for Some Particular Dynamical Systems," Methodology and Computing in Applied Probability, Springer, vol. 20(2), pages 553-562, June.
    • Handle: RePEc:spr:metcap:v:20:y:2018:i:2:d:10.1007_s11009-017-9573-4
    DOI: 10.1007/s11009-017-9573-4
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    References listed on IDEAS

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    1. Freitas, Ana Cristina Moreira & Freitas, Jorge Milhazes, 2008. "On the link between dependence and independence in extreme value theory for dynamical systems," Statistics & Probability Letters, Elsevier, vol. 78(9), pages 1088-1093, July.
    2. Yannick Malevergne & Vladilen Pisarenko & Didier Sornette, 2006. "On the Power of Generalized Extreme Value (GEV) and Generalized Pareto Distribution (GPD) Estimators for Empirical Distributions of Stock Returns," Post-Print hal-02311834, HAL.
    3. Haiman, George, 2003. "Extreme values of the tent map process," Statistics & Probability Letters, Elsevier, vol. 65(4), pages 451-456, December.
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