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Extreme values of the tent map process

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  • Haiman, George

Abstract

Let X0 be uniformly distributed on [0,1] and define the "tent map process" by Xn+1=1-2Xn-1, n[greater-or-equal, slanted]0. Let Mn=max(X1,...,Xn). We obtain the following results: For any integers n and k[greater-or-equal, slanted]1 we havewith the convention Cpq=0 if p 0 we have limk-->[infinity] P{M[[lambda]2k][less-than-or-equals, slant]1-2-k}=e-[lambda] (Theorem 2).

Suggested Citation

  • Haiman, George, 2003. "Extreme values of the tent map process," Statistics & Probability Letters, Elsevier, vol. 65(4), pages 451-456, December.
    • Handle: RePEc:eee:stapro:v:65:y:2003:i:4:p:451-456
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    References listed on IDEAS

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    1. M. S. Bartlett, 1990. "Chance or Chaos?," Journal of the Royal Statistical Society Series A, Royal Statistical Society, vol. 153(3), pages 321-330, May.
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    Cited by:

    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. 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. 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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