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On the link between dependence and independence in extreme value theory for dynamical systems

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  • Freitas, Ana Cristina Moreira
  • Freitas, Jorge Milhazes

Abstract

We reformulate the standard conditions that allow to reduce the study of extremes for dependent sequences to the classical extreme value theory. Essentially, we weaken the mixing type condition in such a way that, in the context of dynamical systems, it should follow from decay of correlations.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:stapro:v:78:y:2008:i:9:p:1088-1093
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    References listed on IDEAS

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    1. 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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    Cited by:

    1. Freitas, Ana Cristina Moreira & Freitas, Jorge Milhazes & Todd, Mike, 2015. "Speed of convergence for laws of rare events and escape rates," Stochastic Processes and their Applications, Elsevier, vol. 125(4), pages 1653-1687.
    2. 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.
    3. Angel, Omer & Matzavinos, Anastasios & Roitershtein, Alexander, 2019. "Limit theorem for the Robin Hood game," Statistics & Probability Letters, Elsevier, vol. 149(C), pages 9-15.
    4. Faranda, Davide & Freitas, Jorge Milhazes & Guiraud, Pierre & Vaienti, Sandro, 2015. "Sampling local properties of attractors via Extreme Value Theory," Chaos, Solitons & Fractals, Elsevier, vol. 74(C), pages 55-66.
    5. Livieri, Giulia & Lillo, Fabrizio & Marmi, Stefano & Solomko, Anton & Vaienti, Sandro, 2023. "Unimodal maps perturbed by heteroscedastic noise: an application to a financial systems," LSE Research Online Documents on Economics 120290, London School of Economics and Political Science, LSE Library.
    6. Freitas, Ana Cristina Moreira & Freitas, Jorge Milhazes & Todd, Mike & Vaienti, Sandro, 2016. "Rare events for the Manneville–Pomeau map," Stochastic Processes and their Applications, Elsevier, vol. 126(11), pages 3463-3479.
    7. Freitas, Ana Cristina Moreira, 2009. "Statistics of the maximum for the tent map," Chaos, Solitons & Fractals, Elsevier, vol. 42(1), pages 604-608.

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    1. 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.
    2. Freitas, Ana Cristina Moreira, 2009. "Statistics of the maximum for the tent map," Chaos, Solitons & Fractals, Elsevier, vol. 42(1), pages 604-608.

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