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Mixing Properties and Central Limit Theorem for a Class of Non‐Identical Piecewise Monotonic C 2 — Transformations
Author(s) -
Heinrich Lothar
Publication year - 1996
Publication title -
mathematische nachrichten
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.913
H-Index - 50
eISSN - 1522-2616
pISSN - 0025-584X
DOI - 10.1002/mana.3211810107
Subject(s) - mathematics , lipschitz continuity , mixing (physics) , lebesgue integration , central limit theorem , unit interval , lebesgue measure , sequence (biology) , monotonic function , piecewise , bounded function , limit (mathematics) , interval (graph theory) , combinatorics , pure mathematics , mathematical analysis , statistics , biology , genetics , physics , quantum mechanics
For a sequence T (1) , T (2) ,…of piecewise monotonic C 2 ‐ transformations of the unit interval I onto itself, we prove exponential ψ‐ mixing, an almost Markov property and other higher‐order mixing properties. Furthermore, we obtain optimal rates of convergence in the central limit Theorem and large deviation relations for the sequence f k o T ( k −1)o…o T (1) , k =1, 2, …, provided that the real‐valued functions f 1 , f 2 ,…on I are of bounded variation and the corresponding probability measure on I possesses a positive, Lipschitz‐continuous Lebesgue density.