Hierarchical structures associated with order functions

Deli Li and Yongcheng Qi

Statistics & Probability Letters, 2007, vol. 77, issue 5, 525-529

Abstract: Let k and m be two fixed positive integers with k[greater-or-equal, slanted]3 and 1 [xi]}. Define the hierarchical sequence of random variables Xn,1,n[greater-or-equal, slanted]0 by Xn+1,j=f(Xn,1+(j-1)k,Xn,2+(j-1)k,...,Xn,k+(j-1)k) with {X0,j,j[greater-or-equal, slanted]1} being independent random variables identically distributed as X0. In this note it is shown that and a.s. and a.s. It follows that a.s. if and only if [lambda]1=[lambda]2=[lambda]. This result generalizes and improves Propositions 4.3 and 4.4 of Li and Rogers [1999. Asymptotic behavior for iterated functions of random variables. Ann. Appl. Probab. 9, 1175-1201].

Keywords: Asymptotic; behavior; Hierarchical; structures; Order; functions (search for similar items in EconPapers)
Date: 2007
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