On central limit theorems, modulus of continuity and Diophantine type for irrational rotations

DOI10.1007/BF02788838zbMath0790.60027MaRDI QIDQ1317276

Michael T. Lacey

Publication date: 18 April 1994

Published in: Journal d'Analyse Mathématique (Search for Journal in Brave)

zbMATH Keywords

Brownian motionmodulus of continuityself-similar processescentral limit theoremsnumber-theoretic properties

Mathematics Subject Classification ID

Central limit and other weak theorems (60F05) Sample path properties (60G17) Diophantine approximation in probabilistic number theory (11K60)

Related Items (11)

Ergodic averages with deterministic weights ⋮ On weak convergence of sampled dynamical systems. ⋮ Sums of continuous and differentiable functions in dynamical systems ⋮ Flexibility of statistical properties for smooth systems satisfying the central limit theorem ⋮ Temporal distributional limit theorems for dynamical systems ⋮ On the CLT for rotations and BV functions ⋮ A borderline Gaussian random Fourier series for the sample convergence in variation ⋮ Fractional Poisson equations and ergodic theorems for fractional coboundaries ⋮ LIMIT THEOREMS FOR SAMPLED DYNAMICAL SYSTEMS ⋮ Local limit theorem in deterministic systems ⋮ Invariance principles and Gaussian approximation for strictly stationary processes

Cites Work

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• Ergodic properties of invariant measures for piecewise monotonic transformations
• Some properties of trigonometric series whose terms have random signs
• ℤⁿ and ℝⁿ cocycle extensions and complementary algebras
• On the Central Limit Theorem for Dynamical Systems
• On Weak Convergence in Dynamical Systems to Self-Similar Processes with Spectral Representation
• Fractional Brownian Motions, Fractional Noises and Applications

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