Mixing Properties and Central Limit Theorem for a Class of Non-Identical Piecewise Monotonic C 2 - Transformations

DOI10.1002/mana.3211810107zbMath0863.60023OpenAlexW2158245851MaRDI QIDQ4892480

Lothar Heinrich

Publication date: 10 June 1997

Published in: Mathematische Nachrichten (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1002/mana.3211810107

zbMATH Keywords

central limit theoremlarge deviationsPerron-Frobenius operatorstransformations of the unit interval\(\Psi\)-mixingalmost Markov propertygeneralized \(f\)-expansions

Mathematics Subject Classification ID

Central limit and other weak theorems (60F05) Large deviations (60F10) Ergodic theory (37A99) Low-dimensional dynamical systems (37E99)

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Cites Work

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• On transformations of distribution functions on the unit interval -- a generalization of the Gauß-Kuzmin-Lévy theorem
• Central limit asymptotics for shifts of finite type
• A central limit theorem of mixed type for a class of 1-dimensional transformations
• Random f-expansions
• Ergodic properties of invariant measures for piecewise monotonic transformations
• Representations of real numbers by infinite series
• Infinitely Divisible Distributions as Limit Laws for Sums of Random Variables Connected in a Markov Chain
• Probabilities of Large Deviations for Random Vectors
• Rates of Convergence in Stable Limit Theorems for Sums of Exponentially Ψ-mixing Random Variables with an Application to Metric Theory of Continued Fractions
• A method for the derivation of limit theorems for sums of weakly dependent random variables:a survey
• On Some Limit Theorems for Continued Fractions
• Mixing sequences of random variables and probablistic number theory

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