Extreme values of the tent map process

George Haiman

Statistics & Probability Letters, 2003, vol. 65, issue 4, 451-456

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).

Keywords: Logistic; map; Tent; map; Dynamical; systems; Extremes (search for similar items in EconPapers)
Date: 2003
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Citations: View citations in EconPapers (3)

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