Extreme values of the tent map process

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<q and where [x] denotes the integer part of x (Theorem 1). For any [lambda]>0 we have limk-->[infinity] P{M[[lambda]2k][less-than-or-equals, slant]1-2-k}=e-[lambda] (Theorem 2).

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Year of publication:	2003
Authors:	Haiman, George
Published in:	Statistics & Probability Letters. - Elsevier, ISSN 0167-7152. - Vol. 65.2003, 4, p. 451-456
Publisher:	Elsevier
Keywords:	Logistic map Tent map Dynamical systems Extremes

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Type of publication:	Article
Source:	RePEc - Research Papers in Economics

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